यदि (f(x)=x+2) और (g(x)=3x), तो ((f+g)(x)) क्या होगा?
If (f(x)=x+2) and (g(x)=3x), what is ((f+g)(x))?
#algebra
#real functions
#function addition
#class 11
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A (4x+2)
B (3x+2)
C (4x-2)
D (x+5)
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Explanation
Simple Explanation
योग में समान (x) पद जोड़े जाते हैं, इसलिए ((f+g)(x)=x+2+3x=4x+2)। परीक्षा में पहले कोष्ठक खोलें। / In addition, like (x) terms are added, so ((f+g)(x)=x+2+3x=4x+2). In exams, open brackets first.
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यदि (f(x)=5x-1) और (g(x)=2x+4), तो ((f-g)(x)) ज्ञात कीजिए।
If (f(x)=5x-1) and (g(x)=2x+4), find ((f-g)(x)).
#algebra
#real functions
#function subtraction
#class 11
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A (3x-5)
B (7x+3)
C (3x+5)
D (7x-5)
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Explanation
Simple Explanation
((f-g)(x)=(5x-1)-(2x+4)=3x-5)। घटाने में दूसरे फलन के सभी चिह्न बदलें। / ((f-g)(x)=(5x-1)-(2x+4)=3x-5). In subtraction, change every sign of the second function.
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यदि (f(x)=x+1) और (g(x)=x-1), तो ((fg)(x)) क्या है?
If (f(x)=x+1) and (g(x)=x-1), what is ((fg)(x))?
#algebra
#real functions
#function product
#class 11
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A \(x^2-1\)
B \(x^2+1\)
C (2x)
D \(x^2-2x+1\)
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Correct Answer
A. \(x^2-1\)
Explanation
Simple Explanation
गुणन में ((fg)(x)=f(x)g(x)), इसलिए ((x+1)(x-1)=x-2 -1)। पहचान \(a^2-b^2\) याद रखें। / In multiplication, ((fg)(x)=f(x)g(x)), so ((x+1)(x-1)=x-2 -1). Remember the identity \(a^2-b^2\).
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यदि (f(x)=2x+6) और (g(x)=2), तो (\left\(\frac{f}{g}\right\)(x)) क्या होगा?
If (f(x)=2x+6) and (g(x)=2), what is (\left\(\frac{f}{g}\right\)(x))?
#algebra
#real functions
#function quotient
#class 11
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A (x+3)
B (2x+3)
C (x+6)
D (4x+12)
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Explanation
Simple Explanation
भाग में (\left\(\frac{f}{g}\right\)(x)=\frac{2x+6}{2}=x+3)। हर शून्य नहीं होना चाहिए। / In division, (\left\(\frac{f}{g}\right\)(x)=\frac{2x+6}{2}=x+3). The denominator must not be zero.
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यदि (f(x)=x-2 ) और (g(x)=4), तो ((f+g)(2)) का मान क्या है?
If (f(x)=x-2 ) and (g(x)=4), what is the value of ((f+g)(2))?
#algebra
#real functions
#value based
#class 11
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A (8)
B (6)
C (12)
D (4)
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Explanation
Simple Explanation
((f+g)(2)=f(2)+g(2)=4+4=8)। पहले फलन जोड़ें या सीधे मान रखें। / ((f+g)(2)=f(2)+g(2)=4+4=8). You may add functions first or substitute directly.
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यदि (f(x)=3x) और (g(x)=x+5), तो ((f-g)(1)) का मान ज्ञात कीजिए।
If (f(x)=3x) and (g(x)=x+5), find the value of ((f-g)(1)).
#algebra
#real functions
#function subtraction
#value
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A (-3)
B (3)
C (9)
D (-1)
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Explanation
Simple Explanation
((f-g)(1)=f(1)-g(1)=3-6=-3)। मान रखने से पहले सही क्रम देखें। / ((f-g)(1)=f(1)-g(1)=3-6=-3). Check the correct order before substituting.
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यदि (f(x)=x+2) और (g(x)=x+3), तो ((fg)(1)) क्या होगा?
If (f(x)=x+2) and (g(x)=x+3), what is ((fg)(1))?
#algebra
#real functions
#function product
#value
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A (12)
B (7)
C (6)
D (10)
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Explanation
Simple Explanation
((fg)(1)=f(1)g(1)=3\times4=12)। गुणन फलन में मानों का गुणा करें। / ((fg)(1)=f(1)g(1)=3\times4=12). In product of functions, multiply the values.
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यदि (f(x)=x-2 -4) और (g(x)=x-2), तो (\left\(\frac{f}{g}\right\)(3)) का मान क्या है?
If (f(x)=x-2 -4) and (g(x)=x-2), what is the value of (\left\(\frac{f}{g}\right\)(3))?
#algebra
#real functions
#function quotient
#value
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A (5)
B (1)
C (9)
D (7)
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Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(3)=\frac{9-4}{3-2}=5)। भाग में हर का मान शून्य नहीं होना चाहिए। / (\left\(\frac{f}{g}\right\)(3)=\frac{9-4}{3-2}=5). In division, the denominator value must not be zero.
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यदि (f(x)=x-2 +1) और (g(x)=2x), तो ((f+g)(x)) किसके बराबर है?
If (f(x)=x-2 +1) and (g(x)=2x), then ((f+g)(x)) is equal to which expression?
#algebra
#real functions
#function addition
#polynomial
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A \(x^2+2x+1\)
B \(x^2-2x+1\)
C \(2x^3+1\)
D \(x^2+3x\)
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Correct Answer
A. \(x^2+2x+1\)
Explanation
Simple Explanation
((f+g)(x)=x-2 +1+2x=x-2 +2x+1)। पदों को घटते घात क्रम में लिखना अच्छा रहता है। / ((f+g)(x)=x-2 +1+2x=x-2 +2x+1). Writing terms in descending powers is a good exam habit.
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यदि (f(x)=4x+7) और (g(x)=x-3), तो ((f-g)(x)) क्या होगा?
If (f(x)=4x+7) and (g(x)=x-3), what is ((f-g)(x))?
#algebra
#real functions
#subtraction
#linear functions
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A (3x+10)
B (5x+4)
C (3x+4)
D (5x+10)
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Correct Answer
A. (3x+10)
Explanation
Simple Explanation
((f-g)(x)=(4x+7)-(x-3)=3x+10)। ऋण चिह्न को पूरे कोष्ठक पर लगाएँ। / ((f-g)(x)=(4x+7)-(x-3)=3x+10). Apply the minus sign to the whole bracket.
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यदि (f(x)=2x) और (g(x)=x-2 ), तो ((fg)(x)) क्या है?
If (f(x)=2x) and (g(x)=x-2 ), what is ((fg)(x))?
#algebra
#real functions
#product
#exponents
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A \(2x^3\)
B \(2x^2\)
C \(x^3+2\)
D \(2x+x^2\)
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Correct Answer
A. \(2x^3\)
Explanation
Simple Explanation
((fg)(x)=2x\cdot x-2 =2x-3 )। समान आधार में घातें जुड़ती हैं। / ((fg)(x)=2x\cdot x-2 =2x-3 ). For the same base, powers are added in multiplication.
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यदि (f(x)=6x-2 ) और (g(x)=3x), तो (\left\(\frac{f}{g}\right\)(x)) क्या होगा, जहाँ \(x\neq0\)?
If (f(x)=6x-2 ) and (g(x)=3x), what is (\left\(\frac{f}{g}\right\)(x)), where \(x\neq0\)?
#algebra
#real functions
#quotient
#domain
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A (2x)
B (3x)
C \(2x^2\)
D \(9x^3\)
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Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(x)=\frac{6x-2 }{3x}=2x), क्योंकि \(x\neq0\)। भाग में पहले शर्त जाँचें। / (\left\(\frac{f}{g}\right\)(x)=\frac{6x-2 }{3x}=2x), because \(x\neq0\). In quotient questions, check the condition first.
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यदि (f(x)=x+4), तो ((2f)(x)) क्या होगा?
If (f(x)=x+4), what is ((2f)(x))?
#algebra
#real functions
#scalar multiplication
#class 11
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A (2x+8)
B (x+8)
C (2x+4)
D (x+6)
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Explanation
Simple Explanation
((2f)(x)=2f(x)=2(x+4)=2x+8)। स्थिर गुणन में हर पद से गुणा करें। / ((2f)(x)=2f(x)=2(x+4)=2x+8). In scalar multiplication, multiply every term.
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यदि (f(x)=3x-2), तो ((-f)(x)) किसके बराबर है?
If (f(x)=3x-2), what is ((-f)(x)) equal to?
#algebra
#real functions
#negative function
#signs
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A (-3x+2)
B (3x+2)
C (-3x-2)
D (x-2)
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Correct Answer
A. (-3x+2)
Explanation
Simple Explanation
((-f)(x)=-f(x)=-(3x-2)=-3x+2)। ऋण पूरे फलन पर लगता है। / ((-f)(x)=-f(x)=-(3x-2)=-3x+2). The negative sign applies to the whole function.
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यदि (f(x)=x-2 ), तो ((f+f)(x)) क्या होगा?
If (f(x)=x-2 ), what is ((f+f)(x))?
#algebra
#real functions
#function addition
#common mistake
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A \(2x^2\)
B \(x^4\)
C \(x^2+2\)
D (2x)
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Correct Answer
A. \(2x^2\)
Explanation
Simple Explanation
((f+f)(x)=x-2 +x-2 =2x-2 )। समान पदों को जोड़ें, घातों को नहीं। / ((f+f)(x)=x-2 +x-2 =2x-2 ). Add like terms, not the powers.
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यदि (f(x)=x+1), तो ((ff)(x)) क्या है?
If (f(x)=x+1), what is ((ff)(x))?
#algebra
#real functions
#product
#common mistake
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A \(x^2+2x+1\)
B (2x+2)
C \(x^2+1\)
D (x+2)
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Correct Answer
A. \(x^2+2x+1\)
Explanation
Simple Explanation
((ff)(x)=f(x)f(x)=(x+1)2 =x-2 +2x+1)। ((ff)(x)) को ((f+f)(x)) न समझें। / ((ff)(x)=f(x)f(x)=(x+1)2 =x-2 +2x+1). Do not confuse ((ff)(x)) with ((f+f)(x)).
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यदि (f(x)=x+5) और (g(x)=x+5), तो ((f-g)(x)) क्या होगा?
If (f(x)=x+5) and (g(x)=x+5), what is ((f-g)(x))?
#algebra
#real functions
#equal functions
#subtraction
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A (0)
B (2x+10)
C (x+5)
D (1)
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Explanation
Simple Explanation
दोनों फलन समान हैं, इसलिए ((f-g)(x)=(x+5)-(x+5)=0)। समान फलनों का अंतर शून्य होता है। / Both functions are equal, so ((f-g)(x)=(x+5)-(x+5)=0). The difference of equal functions is zero.
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यदि (f(x)=0) और (g(x)=x-2 +3), तो ((f+g)(x)) क्या होगा?
If (f(x)=0) and (g(x)=x-2 +3), what is ((f+g)(x))?
#algebra
#real functions
#zero function
#addition
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A \(x^2+3\)
B (0)
C \(x^2\)
D \(3x^2\)
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Correct Answer
A. \(x^2+3\)
Explanation
Simple Explanation
शून्य फलन जोड़ने से फलन नहीं बदलता, इसलिए ((f+g)(x)=x-2 +3)। यह योग का पहचान गुण है। / Adding the zero function does not change the function, so ((f+g)(x)=x-2 +3). This is the identity property of addition.
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यदि (f(x)=1) और (g(x)=x-2 -2x), तो ((fg)(x)) क्या होगा?
If (f(x)=1) and (g(x)=x-2 -2x), what is ((fg)(x))?
#algebra
#real functions
#unit function
#product
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A \(x^2-2x\)
B \(x^2-2x+1\)
C (1)
D \(x^2+2x\)
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Correct Answer
A. \(x^2-2x\)
Explanation
Simple Explanation
एकक फलन (1) से गुणा करने पर ((fg)(x)=g(x)) रहता है। गुणन में (1) पहचान तत्व है। / Multiplying by the unit function (1) gives ((fg)(x)=g(x)). In multiplication, (1) is the identity element.
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यदि (f(x)=x-2) और (g(x)=x+2), तो ((f+g)(x)) क्या होगा?
If (f(x)=x-2) and (g(x)=x+2), what is ((f+g)(x))?
#algebra
#real functions
#function addition
#linear functions
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A (2x)
B \(x^2-4\)
C (4)
D (2x+4)
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Explanation
Simple Explanation
((f+g)(x)=(x-2)+(x+2)=2x)। विपरीत स्थिर पद कट जाते हैं। / ((f+g)(x)=(x-2)+(x+2)=2x). Opposite constant terms cancel out.
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यदि (f(x)=x-2 +2x) और (g(x)=x-2 -x), तो ((f-g)(x)) क्या है?
If (f(x)=x-2 +2x) and (g(x)=x-2 -x), what is ((f-g)(x))?
#algebra
#real functions
#polynomial subtraction
#class 11
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A (3x)
B \(2x^2+x\)
C (x)
D \(x^2+3x\)
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Explanation
Simple Explanation
((f-g)(x)=x-2 +2x-\(x^2-x\)=3x)। समान \(x^2\) पद कट जाते हैं। / ((f-g)(x)=x-2 +2x-\(x^2-x\)=3x). The like \(x^2\) terms cancel out.
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यदि (f(x)=x+2) और (g(x)=2x+1), तो ((fg)(0)) का मान क्या होगा?
If (f(x)=x+2) and (g(x)=2x+1), what is the value of ((fg)(0))?
#algebra
#real functions
#product
#value based
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A (2)
B (0)
C (3)
D (1)
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Explanation
Simple Explanation
((fg)(0)=f(0)g(0)=2\cdot1=2)। पहले दोनों फलनों का मान निकालें। / ((fg)(0)=f(0)g(0)=2\cdot1=2). First find the value of both functions.
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यदि (f(x)=x-2 +3) और (g(x)=x-2 -1), तो ((f-g)(2)) क्या है?
If (f(x)=x-2 +3) and (g(x)=x-2 -1), what is ((f-g)(2))?
#algebra
#real functions
#value based
#subtraction
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A (4)
B (8)
C (2)
D (6)
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Explanation
Simple Explanation
((f-g)(2)=f(2)-g(2)=7-3=4)। कभी-कभी पहले सरल करने से समय बचता है। / ((f-g)(2)=f(2)-g(2)=7-3=4). Sometimes simplifying first saves time.
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यदि (f(x)=2x+1) और (g(x)=x-4), तो ((f+g)(-1)) का मान क्या है?
If (f(x)=2x+1) and (g(x)=x-4), what is the value of ((f+g)(-1))?
#algebra
#real functions
#function addition
#negative input
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A (-8)
B (8)
C (-6)
D (0)
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Explanation
Simple Explanation
((f+g)(-1)=f(-1)+g(-1)=-1+(-5)=-6) नहीं, ध्यान दें (f(-1)=-1) और कुल (-6) है। सही विकल्प (-6) होना चाहिए। / ((f+g)(-1)=f(-1)+g(-1)=-1+(-5)=-6). Check signs carefully for negative input.
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यदि (f(x)=3x+2) और (g(x)=x+1), तो (\left\(\frac{f}{g}\right\)(1)) क्या होगा?
If (f(x)=3x+2) and (g(x)=x+1), what is (\left\(\frac{f}{g}\right\)(1))?
#algebra
#real functions
#quotient
#value based
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A \(\frac{5}{2}\)
B (5)
C (2)
D \(\frac{2}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{5}{2}\)
Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(1)=\frac{f(1)}{g(1)}=\frac{5}{2})। हर का मान (2) है, इसलिए भाग संभव है। / (\left\(\frac{f}{g}\right\)(1)=\frac{f(1)}{g(1)}=\frac{5}{2}). The denominator value is (2), so division is allowed.
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यदि (f(x)=\sqrt{x}) और (g(x)=x+1), तो ((f+g)(4)) का मान क्या होगा?
If (f(x)=\sqrt{x}) and (g(x)=x+1), what is the value of ((f+g)(4))?
#algebra
#real functions
#radical function
#value
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A (7)
B (5)
C (6)
D (9)
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Explanation
Simple Explanation
((f+g)(4)=\sqrt{4}+5=2+5=7)। मूल वाले फलन में परिभाषित मान ही रखें। / ((f+g)(4)=\sqrt{4}+5=2+5=7). For radical functions, substitute only defined values.
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यदि (f(x)=x-2 ) और (g(x)=\sqrt{x}), तो ((fg)(9)) क्या होगा?
If (f(x)=x-2 ) and (g(x)=\sqrt{x}), what is ((fg)(9))?
#algebra
#real functions
#product
#radical function
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A (243)
B (81)
C (27)
D (729)
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Explanation
Simple Explanation
((fg)(9)=92 \cdot\sqrt{9}=81\cdot3=243)। गुणन से पहले अलग-अलग मान निकालना आसान है। / ((fg)(9)=92 \cdot\sqrt{9}=81\cdot3=243). Finding separate values first is easier.
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यदि (f(x)=\frac{1}{x}) और (g(x)=x), तो ((fg)(2)) का मान क्या है?
If (f(x)=\frac{1}{x}) and (g(x)=x), what is the value of ((fg)(2))?
#algebra
#real functions
#reciprocal function
#product
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A (1)
B (2)
C \(\frac{1}{2}\)
D (4)
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Explanation
Simple Explanation
((fg)(2)=\frac{1}{2}\cdot2=1)। भिन्न फलन में \(x\neq0\) शर्त याद रखें। / ((fg)(2)=\frac{1}{2}\cdot2=1). Remember the condition \(x\neq0\) for reciprocal functions.
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यदि (f(x)=x+6) और (g(x)=x+2), तो (\left\(\frac{f}{g}\right\)(0)) क्या है?
If (f(x)=x+6) and (g(x)=x+2), what is (\left\(\frac{f}{g}\right\)(0))?
#algebra
#real functions
#quotient
#value
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A (3)
B (6)
C (2)
D \(\frac{1}{3}\)
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Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(0)=\frac{6}{2}=3)। हर (0) नहीं है, इसलिए मान मान्य है। / (\left\(\frac{f}{g}\right\)(0)=\frac{6}{2}=3). The denominator is not (0), so the value is valid.
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यदि (f(x)=x-1) और (g(x)=x+1), तो ((fg)(x)) किस पहचान से सरल होगा?
If (f(x)=x-1) and (g(x)=x+1), which identity simplifies ((fg)(x))?
#algebra
#real functions
#identity
#product
50 50-50 2 wrong hide
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A \(a^2-b^2\)
B \(a^2+2ab+b^2\)
C \(a^3+b^3\)
D \(a^2-2ab+b^2\)
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Correct Answer
A. \(a^2-b^2\)
Explanation
Simple Explanation
((x-1)(x+1)) में \(a^2-b^2\) पहचान लगती है। इससे ((fg)(x)=x-2 -1) मिलता है। / The identity \(a^2-b^2\) applies to ((x-1)(x+1)). It gives ((fg)(x)=x-2 -1).
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यदि (f(x)=x-2 ) और (g(x)=2x+1), तो ((f+g)(3)) क्या है?
If (f(x)=x-2 ) and (g(x)=2x+1), what is ((f+g)(3))?
#algebra
#real functions
#value
#function addition
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A (16)
B (10)
C (13)
D (22)
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Explanation
Simple Explanation
((f+g)(3)=f(3)+g(3)=9+7=16)। मान रखते समय (2x+1) में (x=3) रखें। / ((f+g)(3)=f(3)+g(3)=9+7=16). Substitute (x=3) in (2x+1) carefully.
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यदि (f(x)=2x-2 ) और (g(x)=x-2 +5), तो ((f-g)(x)) क्या होगा?
If (f(x)=2x-2 ) and (g(x)=x-2 +5), what is ((f-g)(x))?
#algebra
#real functions
#polynomial
#subtraction
50 50-50 2 wrong hide
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A \(x^2-5\)
B \(3x^2+5\)
C \(x^2+5\)
D \(3x^2-5\)
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Correct Answer
A. \(x^2-5\)
Explanation
Simple Explanation
((f-g)(x)=2x-2 -\(x^2+5\)=x-2 -5)। कोष्ठक हटाते समय चिह्न बदलें। / ((f-g)(x)=2x-2 -\(x^2+5\)=x-2 -5). Change signs while removing the bracket.
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यदि (f(x)=x+3) और (g(x)=x), तो ((fg)(x)) क्या है?
If (f(x)=x+3) and (g(x)=x), what is ((fg)(x))?
#algebra
#real functions
#product
#distributive law
50 50-50 2 wrong hide
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A \(x^2+3x\)
B (2x+3)
C \(x^2+3\)
D \(3x^2\)
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Correct Answer
A. \(x^2+3x\)
Explanation
Simple Explanation
((fg)(x)=(x+3)x=x-2 +3x)। वितरक नियम से गुणा करें। / ((fg)(x)=(x+3)x=x-2 +3x). Use the distributive law for multiplication.
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यदि (f(x)=2x-3) और (g(x)=x+4), तो ((f+g)(x)) क्या होगा?
If (f(x)=2x-3) and (g(x)=x+4), what is ((f+g)(x))?
#algebra
#real functions
#linear functions
#addition
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A (3x+1)
B (x+1)
C (3x-7)
D \(2x^2+x-12\)
Explanation opens after your attempt
Explanation
Simple Explanation
((f+g)(x)=(2x-3)+(x+4)=3x+1)। समान पदों को अलग-अलग जोड़ें। / ((f+g)(x)=(2x-3)+(x+4)=3x+1). Add like terms separately.
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यदि (f(x)=5) और (g(x)=x-2 ), तो ((f-g)(x)) क्या है?
If (f(x)=5) and (g(x)=x-2 ), what is ((f-g)(x))?
#algebra
#real functions
#constant function
#subtraction
50 50-50 2 wrong hide
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A \(5-x^2\)
B \(x^2-5\)
C \(5x^2\)
D \(x^2+5\)
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Correct Answer
A. \(5-x^2\)
Explanation
Simple Explanation
((f-g)(x)=5-x-2 )। क्रम बदलने से उत्तर \(x^2-5\) हो जाएगा, इसलिए क्रम महत्वपूर्ण है। / ((f-g)(x)=5-x-2 ). If the order changes, the answer becomes \(x^2-5\), so order is important.
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यदि (f(x)=x-2 -9) और (g(x)=x+3), तो (\left\(\frac{f}{g}\right\)(x)) का सरल रूप क्या है, जहाँ \(x\neq-3\)?
If (f(x)=x-2 -9) and (g(x)=x+3), what is the simplified form of (\left\(\frac{f}{g}\right\)(x)), where \(x\neq-3\)?
#algebra
#real functions
#quotient
#factorization
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A (x-3)
B (x+3)
C \(x^2-3\)
D (x-9)
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Explanation
Simple Explanation
(\frac{x-2 -9}{x+3}=\frac{(x-3)(x+3)}{x+3}=x-3), जहाँ \(x\neq-3\)। काटने से पहले शर्त लिखें। / (\frac{x-2 -9}{x+3}=\frac{(x-3)(x+3)}{x+3}=x-3), where \(x\neq-3\). Write the condition before cancellation.
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यदि (f(x)=x-2 +2x+1) और (g(x)=x+1), तो (\left\(\frac{f}{g}\right\)(x)) क्या होगा, जहाँ \(x\neq-1\)?
If (f(x)=x-2 +2x+1) and (g(x)=x+1), what is (\left\(\frac{f}{g}\right\)(x)), where \(x\neq-1\)?
#algebra
#real functions
#quotient
#perfect square
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A (x+1)
B (x-1)
C \(x^2+1\)
D (2x+1)
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Explanation
Simple Explanation
क्योंकि (x-2 +2x+1=(x+1)2 ), इसलिए भागफल (x+1) है। (x=-1) हटाना न भूलें। / Since (x-2 +2x+1=(x+1)2 ), the quotient is (x+1). Do not forget to exclude (x=-1).
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यदि (f(x)=x+2) और (g(x)=x-5), तो ((f+g)(5)) क्या होगा?
If (f(x)=x+2) and (g(x)=x-5), what is ((f+g)(5))?
#algebra
#real functions
#value
#addition
50 50-50 2 wrong hide
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A (7)
B (12)
C (0)
D (10)
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Explanation
Simple Explanation
((f+g)(5)=f(5)+g(5)=7+0=7)। किसी एक फलन का मान शून्य हो तो भी जोड़ सामान्य रहता है। / ((f+g)(5)=f(5)+g(5)=7+0=7). Even if one function value is zero, addition remains normal.
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यदि (f(x)=4x) और (g(x)=x+2), तो ((fg)(2)) का मान ज्ञात कीजिए।
If (f(x)=4x) and (g(x)=x+2), find the value of ((fg)(2)).
#algebra
#real functions
#product
#value
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A (32)
B (16)
C (24)
D (8)
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Explanation
Simple Explanation
((fg)(2)=f(2)g(2)=8\cdot4=32)। गुणन में दोनों मानों को अलग-अलग निकालें। / ((fg)(2)=f(2)g(2)=8\cdot4=32). In product questions, find both values separately.
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यदि (f(x)=x-2 -1) और (g(x)=x-2 +1), तो ((f+g)(x)) क्या है?
If (f(x)=x-2 -1) and (g(x)=x-2 +1), what is ((f+g)(x))?
#algebra
#real functions
#polynomial addition
#class 11
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A \(2x^2\)
B (2)
C \(x^4-1\)
D \(2x^2+2\)
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Correct Answer
A. \(2x^2\)
Explanation
Simple Explanation
((f+g)(x)=x-2 -1+x-2 +1=2x-2 )। स्थिर पद (-1) और (1) कट जाते हैं। / ((f+g)(x)=x-2 -1+x-2 +1=2x-2 ). The constant terms (-1) and (1) cancel out.
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यदि (f(x)=3x-2 +1) और (g(x)=x-2 -4), तो ((f-g)(x)) क्या होगा?
If (f(x)=3x-2 +1) and (g(x)=x-2 -4), what is ((f-g)(x))?
#algebra
#real functions
#subtraction
#polynomial
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A \(2x^2+5\)
B \(4x^2-3\)
C \(2x^2-3\)
D \(4x^2+5\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+5\)
Explanation
Simple Explanation
((f-g)(x)=3x-2 +1-\(x^2-4\)=2x-2 +5)। ऋण को अंदर के दोनों पदों पर लगाएँ। / ((f-g)(x)=3x-2 +1-\(x^2-4\)=2x-2 +5). Apply the minus sign to both inner terms.
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यदि (f(x)=x+1) और (g(x)=2), तो ((fg)(x)) क्या है?
If (f(x)=x+1) and (g(x)=2), what is ((fg)(x))?
#algebra
#real functions
#constant function
#product
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A (2x+2)
B (x+3)
C (2x+1)
D \(x^2+2\)
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Explanation
Simple Explanation
((fg)(x)=(x+1)\cdot2=2x+2)। स्थिर फलन से गुणा करने पर हर पद गुणित होता है। / ((fg)(x)=(x+1)\cdot2=2x+2). Multiplying by a constant function multiplies every term.
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यदि (f(x)=8x+4) और (g(x)=4), तो (\left\(\frac{f}{g}\right\)(x)) क्या होगा?
If (f(x)=8x+4) and (g(x)=4), what is (\left\(\frac{f}{g}\right\)(x))?
#algebra
#real functions
#quotient
#constant function
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A (2x+1)
B (8x+1)
C (2x+4)
D (32x+16)
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Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(x)=\frac{8x+4}{4}=2x+1)। अंश के हर पद को (4) से भाग दें। / (\left\(\frac{f}{g}\right\)(x)=\frac{8x+4}{4}=2x+1). Divide every numerator term by (4).
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यदि (f(x)=x-7) और (g(x)=7-x), तो ((f+g)(x)) क्या होगा?
If (f(x)=x-7) and (g(x)=7-x), what is ((f+g)(x))?
#algebra
#real functions
#additive inverse
#addition
50 50-50 2 wrong hide
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A (0)
B (2x-14)
C (14)
D \(x^2-49\)
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Explanation
Simple Explanation
((f+g)(x)=(x-7)+(7-x)=0)। ये फलन एक-दूसरे के योगात्मक प्रतिलोम हैं। / ((f+g)(x)=(x-7)+(7-x)=0). These functions are additive inverses of each other.
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यदि (f(x)=2x+5) और (g(x)=2x-5), तो ((f-g)(x)) क्या होगा?
If (f(x)=2x+5) and (g(x)=2x-5), what is ((f-g)(x))?
#algebra
#real functions
#subtraction
#linear functions
50 50-50 2 wrong hide
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A (10)
B (4x)
C (4x+10)
D (0)
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Explanation
Simple Explanation
((f-g)(x)=2x+5-(2x-5)=10)। (x) पद कट जाते हैं। / ((f-g)(x)=2x+5-(2x-5)=10). The (x) terms cancel out.
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यदि (f(x)=x-2 ) और (g(x)=x-3 ), तो ((fg)(x)) क्या है?
If (f(x)=x-2 ) and (g(x)=x-3 ), what is ((fg)(x))?
#algebra
#real functions
#product
#exponents
50 50-50 2 wrong hide
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A \(x^5\)
B \(x^6\)
C \(2x^3\)
D \(x^3+x^2\)
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Correct Answer
A. \(x^5\)
Explanation
Simple Explanation
((fg)(x)=x-2 \cdot x-3 =x-5 )। समान आधार के गुणन में घातें जुड़ती हैं। / ((fg)(x)=x-2 \cdot x-3 =x-5 ). In multiplication with the same base, powers are added.
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यदि (f(x)=x-4 ) और (g(x)=x-2 ), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq0\)?
If (f(x)=x-4 ) and (g(x)=x-2 ), what is (\left\(\frac{f}{g}\right\)(x)), where \(x\neq0\)?
#algebra
#real functions
#quotient
#exponents
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A \(x^2\)
B \(x^6\)
C \(x^8\)
D (x)
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Correct Answer
A. \(x^2\)
Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(x)=\frac{x-4 }{x-2 }=x-2 ), जहाँ \(x\neq0\)। समान आधार में भाग करते समय घातें घटती हैं। / (\left\(\frac{f}{g}\right\)(x)=\frac{x-4 }{x-2 }=x-2 ), where \(x\neq0\). In division with the same base, powers are subtracted.
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यदि (f(x)=x+1) और (g(x)=x+2), तो ((f+g)(x)) का डोमेन क्या होगा, यदि दोनों का डोमेन \(\mathbb{R}\) है?
If (f(x)=x+1) and (g(x)=x+2), what is the domain of ((f+g)(x)), if both have domain \(\mathbb{R}\)?
#algebra
#real functions
#domain
#function addition
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A \(\mathbb{R}\)
B \(\mathbb{R}-{0}\)
C ({1,2})
D \(\emptyset\)
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Correct Answer
A. \(\mathbb{R}\)
Explanation
Simple Explanation
दोनों रैखिक फलन पूरे \(\mathbb{R}\) पर परिभाषित हैं, इसलिए योग का डोमेन भी \(\mathbb{R}\) है। डोमेन में साझा मान देखें। / Both linear functions are defined on all \(\mathbb{R}\), so the domain of the sum is also \(\mathbb{R}\). Check common allowed values for domain.
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यदि (f(x)=\frac{1}{x}) और (g(x)=x+1), तो ((f+g)(x)) का डोमेन क्या है?
If (f(x)=\frac{1}{x}) and (g(x)=x+1), what is the domain of ((f+g)(x))?
#algebra
#real functions
#domain
#reciprocal function
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A \(\mathbb{R}-{0}\)
B \(\mathbb{R}\)
C \(\mathbb{R}-{-1}\)
D ({0})
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{0}\)
Explanation
Simple Explanation
\(\frac{1}{x}\) में (x=0) मान्य नहीं है, इसलिए योग का डोमेन \(\mathbb{R}-{0}\) है। साझा डोमेन लें। / In \(\frac{1}{x}\), (x=0) is not allowed, so the domain of the sum is \(\mathbb{R}-{0}\). Take the common domain.
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यदि (f(x)=x+1) और (g(x)=x-3), तो (\left\(\frac{f}{g}\right\)(x)) का डोमेन क्या होगा?
If (f(x)=x+1) and (g(x)=x-3), what will be the domain of (\left\(\frac{f}{g}\right\)(x))?
#algebra
#real functions
#domain
#quotient
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A \(\mathbb{R}-{3}\)
B \(\mathbb{R}\)
C \(\mathbb{R}-{-1}\)
D ({3})
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{3}\)
Explanation
Simple Explanation
भाग में हर (g(x)=x-3) शून्य नहीं होना चाहिए, इसलिए \(x\neq3\)। अतः डोमेन \(\mathbb{R}-{3}\) है। / In division, the denominator (g(x)=x-3) must not be zero, so \(x\neq3\). Hence the domain is \(\mathbb{R}-{3}\).
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यदि (f(x)=2x+3) और (g(x)=x-5), तो ((f+g)(x)) क्या है?
If (f(x)=2x+3) and (g(x)=x-5), what is ((f+g)(x))?
#algebra
#real functions
#function addition
#easy
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A (3x-2)
B (x+8)
C (3x+8)
D \(2x^2-10x+3\)
Explanation opens after your attempt
Explanation
Simple Explanation
((f+g)(x)=(2x+3)+(x-5)=3x-2)। जोड़ते समय समान पदों को ही जोड़ें। / ((f+g)(x)=(2x+3)+(x-5)=3x-2). While adding, combine only like terms.
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यदि (f(x)=7x-4) और (g(x)=2x+9), तो ((f-g)(x)) ज्ञात कीजिए।
If (f(x)=7x-4) and (g(x)=2x+9), find ((f-g)(x)).
#algebra
#real functions
#function subtraction
#sign rule
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A (5x+5)
B (5x-13)
C (9x+5)
D (9x-13)
Explanation opens after your attempt
Correct Answer
B. (5x-13)
Explanation
Simple Explanation
((f-g)(x)=(7x-4)-(2x+9)=5x-13)। घटाने में दूसरे कोष्ठक के सभी चिह्न बदलें। / ((f-g)(x)=(7x-4)-(2x+9)=5x-13). In subtraction, change all signs of the second bracket.
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यदि (f(x)=x+6) और (g(x)=x-2), तो ((fg)(x)) क्या होगा?
If (f(x)=x+6) and (g(x)=x-2), what will ((fg)(x)) be?
#algebra
#real functions
#function product
#linear product
50 50-50 2 wrong hide
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A \(x^2+4x-12\)
B (2x+4)
C \(x^2+8x-12\)
D \(x^2-4x-12\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x-12\)
Explanation
Simple Explanation
((fg)(x)=(x+6)(x-2)=x-2 +4x-12)। गुणन में हर पद को सही पद से गुणा करें। / ((fg)(x)=(x+6)(x-2)=x-2 +4x-12). In multiplication, multiply each term correctly.
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यदि (f(x)=4x-2 +8x) और (g(x)=4x), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq0\)?
If (f(x)=4x-2 +8x) and (g(x)=4x), what is (\left\(\frac{f}{g}\right\)(x)), where \(x\neq0\)?
#algebra
#real functions
#function quotient
#domain
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A (x+2)
B (4x+8)
C \(x^2+2x\)
D (2x+1)
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Explanation
Simple Explanation
(\frac{4x-2 +8x}{4x}=\frac{4x(x+2)}{4x}=x+2), जहाँ \(x\neq0\)। काटने से पहले हर की शर्त देखें। / (\frac{4x-2 +8x}{4x}=\frac{4x(x+2)}{4x}=x+2), where \(x\neq0\). Check the denominator condition before cancellation.
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यदि (f(x)=x-2 +2) और (g(x)=3x-1), तो ((f+g)(2)) का मान क्या है?
If (f(x)=x-2 +2) and (g(x)=3x-1), what is the value of ((f+g)(2))?
#algebra
#real functions
#value based
#function addition
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A (9)
B (10)
C (11)
D (13)
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Explanation
Simple Explanation
((f+g)(2)=f(2)+g(2)=6+5=11)। मान रखने के बाद ही जोड़ करें। / ((f+g)(2)=f(2)+g(2)=6+5=11). Add only after substituting the value.
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यदि (f(x)=5x+2) और (g(x)=x-2 ), तो ((f-g)(3)) का मान क्या होगा?
If (f(x)=5x+2) and (g(x)=x-2 ), what will be the value of ((f-g)(3))?
#algebra
#real functions
#function subtraction
#value
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A (8)
B (17)
C (26)
D (-8)
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Explanation
Simple Explanation
((f-g)(3)=f(3)-g(3)=17-9=8)। क्रम बदलने से उत्तर बदल सकता है। / ((f-g)(3)=f(3)-g(3)=17-9=8). Changing the order may change the answer.
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यदि (f(x)=2x-1) और (g(x)=x+4), तो ((fg)(2)) क्या है?
If (f(x)=2x-1) and (g(x)=x+4), what is ((fg)(2))?
#algebra
#real functions
#function product
#value based
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A (9)
B (18)
C (21)
D (24)
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Explanation
Simple Explanation
((fg)(2)=f(2)g(2)=3\cdot6=18)। गुणन में फलनों के मानों का गुणा करें। / ((fg)(2)=f(2)g(2)=3\cdot6=18). In product, multiply the values of the functions.
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यदि (f(x)=x-2 -16) और (g(x)=x-4), तो (\left\(\frac{f}{g}\right\)(5)) का मान क्या है?
If (f(x)=x-2 -16) and (g(x)=x-4), what is the value of (\left\(\frac{f}{g}\right\)(5))?
#algebra
#real functions
#quotient
#value
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A (5)
B (7)
C (9)
D (11)
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Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(5)=\frac{25-16}{5-4}=9)। भाग में हर का मान शून्य नहीं होना चाहिए। / (\left\(\frac{f}{g}\right\)(5)=\frac{25-16}{5-4}=9). In division, the denominator value must not be zero.
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यदि (f(x)=3x-2 ) और (g(x)=2x-2 +1), तो ((f+g)(x)) किसके बराबर है?
If (f(x)=3x-2 ) and (g(x)=2x-2 +1), then ((f+g)(x)) is equal to which expression?
#algebra
#real functions
#polynomial addition
#class 11
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A \(5x^2+1\)
B \(6x^4+1\)
C \(x^2+1\)
D \(5x^4\)
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Correct Answer
A. \(5x^2+1\)
Explanation
Simple Explanation
((f+g)(x)=3x-2 +2x-2 +1=5x-2 +1)। समान घात वाले पद जोड़ें। / ((f+g)(x)=3x-2 +2x-2 +1=5x-2 +1). Add terms with the same power.
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यदि (f(x)=9x-2) और (g(x)=4x-7), तो ((f-g)(x)) क्या होगा?
If (f(x)=9x-2) and (g(x)=4x-7), what is ((f-g)(x))?
#algebra
#real functions
#linear subtraction
#signs
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A (5x+5)
B (13x-9)
C (5x-9)
D (13x+5)
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Explanation
Simple Explanation
((f-g)(x)=9x-2-(4x-7)=5x+5)। (-(-7)) को (+7) लिखें। / ((f-g)(x)=9x-2-(4x-7)=5x+5). Write (-(-7)) as (+7).
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यदि (f(x)=x-3 ) और (g(x)=2x), तो ((fg)(x)) क्या होगा?
If (f(x)=x-3 ) and (g(x)=2x), what will ((fg)(x)) be?
#algebra
#real functions
#product
#exponents
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A \(2x^3\)
B \(x^4\)
C \(2x^4\)
D \(3x^4\)
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Correct Answer
C. \(2x^4\)
Explanation
Simple Explanation
((fg)(x)=x-3 \cdot2x=2x-4 )। समान आधार में गुणा करते समय घातें जोड़ें। / ((fg)(x)=x-3 \cdot2x=2x-4 ). Add powers when multiplying the same base.
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यदि (f(x)=10x-3 ) और (g(x)=5x), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq0\)?
If (f(x)=10x-3 ) and (g(x)=5x), what is (\left\(\frac{f}{g}\right\)(x)), where \(x\neq0\)?
#algebra
#real functions
#quotient
#exponents
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A \(2x^2\)
B \(5x^2\)
C \(2x^3\)
D \(15x^4\)
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Correct Answer
A. \(2x^2\)
Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(x)=\frac{10x-3 }{5x}=2x-2 ), जहाँ \(x\neq0\)। भाग में घातें घटती हैं। / (\left\(\frac{f}{g}\right\)(x)=\frac{10x-3 }{5x}=2x-2 ), where \(x\neq0\). In division, powers are subtracted.
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यदि (f(x)=x-8), तो ((3f)(x)) क्या है?
If (f(x)=x-8), what is ((3f)(x))?
#algebra
#real functions
#scalar multiplication
#easy
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A (3x-8)
B (x-24)
C (3x-24)
D (x-5)
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Correct Answer
C. (3x-24)
Explanation
Simple Explanation
((3f)(x)=3(x-8)=3x-24)। स्थिर गुणक को सभी पदों से गुणा करें। / ((3f)(x)=3(x-8)=3x-24). Multiply all terms by the scalar.
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यदि (f(x)=4x+6), तो (\left\(\frac{1}{2}f\right\)(x)) क्या होगा?
If (f(x)=4x+6), what will (\left\(\frac{1}{2}f\right\)(x)) be?
#algebra
#real functions
#scalar multiplication
#fraction
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A (2x+3)
B (4x+3)
C (2x+6)
D (8x+12)
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Explanation
Simple Explanation
(\left\(\frac{1}{2}f\right\)(x)=\frac{1}{2}(4x+6)=2x+3)। भिन्न गुणक को हर पद पर लगाएँ। / (\left\(\frac{1}{2}f\right\)(x)=\frac{1}{2}(4x+6)=2x+3). Apply the fractional multiplier to every term.
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यदि (f(x)=2x-2 -5), तो ((-f)(x)) किसके बराबर है?
If (f(x)=2x-2 -5), what is ((-f)(x)) equal to?
#algebra
#real functions
#negative function
#sign rule
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A \(-2x^2+5\)
B \(2x^2+5\)
C \(-2x^2-5\)
D (5-2x)
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Correct Answer
A. \(-2x^2+5\)
Explanation
Simple Explanation
((-f)(x)=-\(2x^2-5\)=-2x-2 +5)। ऋण चिह्न पूरे फलन पर लगता है। / ((-f)(x)=-\(2x^2-5\)=-2x-2 +5). The negative sign applies to the whole function.
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यदि (f(x)=x-2 +4x), तो ((f+f)(x)) क्या होगा?
If (f(x)=x-2 +4x), what will ((f+f)(x)) be?
#algebra
#real functions
#function addition
#common mistake
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A \(x^4+16x^2\)
B \(2x^2+8x\)
C \(x^2+8x\)
D \(2x^2+4x\)
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Correct Answer
B. \(2x^2+8x\)
Explanation
Simple Explanation
((f+f)(x)=2f(x)=2x-2 +8x)। समान फलन जोड़ना (2f) के बराबर है। / ((f+f)(x)=2f(x)=2x-2 +8x). Adding the same function equals (2f).
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यदि (f(x)=x-3), तो ((ff)(x)) क्या है?
If (f(x)=x-3), what is ((ff)(x))?
#algebra
#real functions
#function product
#common mistake
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A (2x-6)
B \(x^2-3\)
C \(x^2-6x+9\)
D \(x^2+6x+9\)
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Correct Answer
C. \(x^2-6x+9\)
Explanation
Simple Explanation
((ff)(x)=f(x)f(x)=(x-3)2 =x-2 -6x+9)। ((ff)(x)) को ((f+f)(x)) न मानें। / ((ff)(x)=f(x)f(x)=(x-3)2 =x-2 -6x+9). Do not treat ((ff)(x)) as ((f+f)(x)).
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यदि (f(x)=2x+10) और (g(x)=2x+10), तो ((f-g)(x)) क्या है?
If (f(x)=2x+10) and (g(x)=2x+10), what is ((f-g)(x))?
#algebra
#real functions
#equal functions
#subtraction
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A (0)
B (4x+20)
C (1)
D (2x+10)
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Explanation
Simple Explanation
समान फलनों का अंतर (0) होता है, इसलिए ((f-g)(x)=0)। परीक्षा में पहले पहचानें कि दोनों फलन समान हैं। / The difference of equal functions is (0), so ((f-g)(x)=0). In exams, first notice if both functions are equal.
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यदि (f(x)=0) और (g(x)=3x-2 -2), तो ((fg)(x)) क्या होगा?
If (f(x)=0) and (g(x)=3x-2 -2), what will ((fg)(x)) be?
#algebra
#real functions
#zero function
#product
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A \(3x^2-2\)
B (0)
C \(3x^2\)
D (2)
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Explanation
Simple Explanation
शून्य फलन से गुणा करने पर ((fg)(x)=0) होता है। गुणन में (0) पूरे गुणनफल को शून्य कर देता है। / Multiplying by the zero function gives ((fg)(x)=0). In multiplication, (0) makes the whole product zero.
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यदि (f(x)=1) और (g(x)=5x-6), तो ((f+g)(x)) क्या है?
If (f(x)=1) and (g(x)=5x-6), what is ((f+g)(x))?
#algebra
#real functions
#constant function
#addition
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A (5x-5)
B (5x-6)
C (5x-7)
D (5x)
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Explanation
Simple Explanation
((f+g)(x)=1+(5x-6)=5x-5)। स्थिर पदों को ध्यान से जोड़ें। / ((f+g)(x)=1+(5x-6)=5x-5). Add constant terms carefully.
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यदि (f(x)=x+9) और (g(x)=9-x), तो ((f+g)(x)) क्या होगा?
If (f(x)=x+9) and (g(x)=9-x), what will ((f+g)(x)) be?
#algebra
#real functions
#function addition
#cancellation
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A (2x)
B (18)
C \(x^2-81\)
D (0)
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Explanation
Simple Explanation
((f+g)(x)=(x+9)+(9-x)=18)। (x) और (-x) कट जाते हैं। / ((f+g)(x)=(x+9)+(9-x)=18). The terms (x) and (-x) cancel out.
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यदि (f(x)=x-2 +5x) और (g(x)=x-2 +2x), तो ((f-g)(x)) क्या है?
If (f(x)=x-2 +5x) and (g(x)=x-2 +2x), what is ((f-g)(x))?
#algebra
#real functions
#polynomial subtraction
#easy
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A \(2x^2+7x\)
B (3x)
C (7x)
D \(x^2+3x\)
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Explanation
Simple Explanation
((f-g)(x)=x-2 +5x-\(x^2+2x\)=3x)। समान \(x^2\) पद कट जाते हैं। / ((f-g)(x)=x-2 +5x-\(x^2+2x\)=3x). The like \(x^2\) terms cancel out.
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यदि (f(x)=x+7) और (g(x)=3x-2), तो ((fg)(1)) का मान क्या है?
If (f(x)=x+7) and (g(x)=3x-2), what is the value of ((fg)(1))?
#algebra
#real functions
#product
#value
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A (8)
B (6)
C (1)
D (14)
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Explanation
Simple Explanation
((fg)(1)=f(1)g(1)=8\cdot1=8)। पहले दोनों मान निकालें। / ((fg)(1)=f(1)g(1)=8\cdot1=8). First find both values.
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यदि (f(x)=x-2 +10) और (g(x)=x-2 +4), तो ((f-g)(1)) क्या है?
If (f(x)=x-2 +10) and (g(x)=x-2 +4), what is ((f-g)(1))?
#algebra
#real functions
#value based
#subtraction
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A (4)
B (5)
C (6)
D (16)
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Explanation
Simple Explanation
((f-g)(1)=f(1)-g(1)=11-5=6)। यहाँ \(x^2\) पद प्रभावी रूप से कट जाते हैं। / ((f-g)(1)=f(1)-g(1)=11-5=6). Here the \(x^2\) terms effectively cancel.
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यदि (f(x)=6x+1) और (g(x)=2x+3), तो (\left\(\frac{f}{g}\right\)(0)) क्या होगा?
If (f(x)=6x+1) and (g(x)=2x+3), what will (\left\(\frac{f}{g}\right\)(0)) be?
#algebra
#real functions
#quotient
#value based
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A \(\frac{1}{3}\)
B (3)
C \(\frac{3}{1}\)
D (0)
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Correct Answer
A. \(\frac{1}{3}\)
Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(0)=\frac{1}{3})। हर (3) है, इसलिए भाग मान्य है। / (\left\(\frac{f}{g}\right\)(0)=\frac{1}{3}). The denominator is (3), so the quotient is valid.
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यदि (f(x)=\sqrt{x+5}) और (g(x)=x), तो ((f+g)(4)) का मान क्या है?
If (f(x)=\sqrt{x+5}) and (g(x)=x), what is the value of ((f+g)(4))?
#algebra
#real functions
#radical function
#value
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A (5)
B (6)
C (7)
D (9)
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Explanation
Simple Explanation
((f+g)(4)=\sqrt{9}+4=3+4=7)। मूल वाले पद में पहले अंदर का मान निकालें। / ((f+g)(4)=\sqrt{9}+4=3+4=7). For a radical term, first find the inside value.
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यदि (f(x)=x-2 +1) और (g(x)=\sqrt{x}), तो ((fg)(4)) क्या होगा?
If (f(x)=x-2 +1) and (g(x)=\sqrt{x}), what will ((fg)(4)) be?
#algebra
#real functions
#product
#radical function
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A (17)
B (34)
C (18)
D (68)
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Explanation
Simple Explanation
((fg)(4)=f(4)g(4)=17\cdot2=34)। अलग-अलग मान निकालना सबसे सुरक्षित तरीका है। / ((fg)(4)=f(4)g(4)=17\cdot2=34). Finding separate values is the safest method.
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यदि (f(x)=\frac{2}{x}) और (g(x)=x-2 ), तो ((fg)(3)) का मान क्या है?
If (f(x)=\frac{2}{x}) and (g(x)=x-2 ), what is the value of ((fg)(3))?
#algebra
#real functions
#reciprocal function
#product
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A (6)
B (9)
C \(\frac{2}{3}\)
D (18)
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Explanation
Simple Explanation
((fg)(3)=\frac{2}{3}\cdot9=6)। भिन्न फलन में \(x\neq0\) शर्त रहती है। / ((fg)(3)=\frac{2}{3}\cdot9=6). A reciprocal-type function keeps the condition \(x\neq0\).
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यदि (f(x)=x+12) और (g(x)=x+3), तो (\left\(\frac{f}{g}\right\)(3)) क्या है?
If (f(x)=x+12) and (g(x)=x+3), what is (\left\(\frac{f}{g}\right\)(3))?
#algebra
#real functions
#quotient
#simplification
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A \(\frac{5}{2}\)
B (5)
C \(\frac{2}{5}\)
D (3)
Explanation opens after your attempt
Correct Answer
A. \(\frac{5}{2}\)
Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(3)=\frac{15}{6}=\frac{5}{2})। अंतिम उत्तर को सरल भिन्न में लिखें। / (\left\(\frac{f}{g}\right\)(3)=\frac{15}{6}=\frac{5}{2}). Write the final answer in simplest fraction form.
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यदि (f(x)=x+4) और (g(x)=x-4), तो ((fg)(x)) को सरल करने के लिए कौन-सी पहचान उपयोगी है?
If (f(x)=x+4) and (g(x)=x-4), which identity is useful to simplify ((fg)(x))?
#algebra
#real functions
#identity
#product
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A \(a^2-b^2\)
B \(a^2+2ab+b^2\)
C \(a^2-2ab+b^2\)
D \(a^3-b^3\)
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Correct Answer
A. \(a^2-b^2\)
Explanation
Simple Explanation
((x+4)(x-4)) में \(a^2-b^2\) लगता है। इससे उत्तर \(x^2-16\) मिलता है। / ((x+4)(x-4)) uses \(a^2-b^2\). It gives the answer \(x^2-16\).
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यदि (f(x)=2x-2 +3) और (g(x)=x+5), तो ((f+g)(1)) क्या है?
If (f(x)=2x-2 +3) and (g(x)=x+5), what is ((f+g)(1))?
#algebra
#real functions
#value
#function addition
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A (6)
B (9)
C (11)
D (12)
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Explanation
Simple Explanation
((f+g)(1)=f(1)+g(1)=5+6=11)। पहले (x=1) रखें, फिर जोड़ें। / ((f+g)(1)=f(1)+g(1)=5+6=11). First put (x=1), then add.
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यदि (f(x)=5x-2 +2) और (g(x)=2x-2 -7), तो ((f-g)(x)) क्या होगा?
If (f(x)=5x-2 +2) and (g(x)=2x-2 -7), what will ((f-g)(x)) be?
#algebra
#real functions
#polynomial subtraction
#signs
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A \(3x^2-5\)
B \(7x^2-5\)
C \(3x^2+9\)
D \(7x^2+9\)
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Correct Answer
C. \(3x^2+9\)
Explanation
Simple Explanation
((f-g)(x)=5x-2 +2-\(2x^2-7\)=3x-2 +9)। ऋण को (-7) पर लगाने से (+7) आता है। / ((f-g)(x)=5x-2 +2-\(2x^2-7\)=3x-2 +9). Applying the minus to (-7) gives (+7).
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यदि (f(x)=x-6) और (g(x)=x), तो ((fg)(x)) क्या है?
If (f(x)=x-6) and (g(x)=x), what is ((fg)(x))?
#algebra
#real functions
#product
#distributive law
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A \(x^2-6x\)
B (2x-6)
C \(x^2-6\)
D \(6x^2\)
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Correct Answer
A. \(x^2-6x\)
Explanation
Simple Explanation
((fg)(x)=(x-6)x=x-2 -6x)। (x) को दोनों पदों से गुणा करें। / ((fg)(x)=(x-6)x=x-2 -6x). Multiply (x) with both terms.
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यदि (f(x)=4x+11) और (g(x)=x-6), तो ((f+g)(x)) क्या है?
If (f(x)=4x+11) and (g(x)=x-6), what is ((f+g)(x))?
#algebra
#real functions
#linear functions
#addition
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A (5x+5)
B (3x+17)
C (5x+17)
D \(4x^2-13x-66\)
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Explanation
Simple Explanation
((f+g)(x)=4x+11+x-6=5x+5)। (x) पद और स्थिर पद अलग-अलग जोड़ें। / ((f+g)(x)=4x+11+x-6=5x+5). Add (x)-terms and constant terms separately.
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यदि (f(x)=8) और (g(x)=x-2 -3x), तो ((f-g)(x)) क्या है?
If (f(x)=8) and (g(x)=x-2 -3x), what is ((f-g)(x))?
#algebra
#real functions
#constant function
#subtraction
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A \(x^2-3x-8\)
B \(8-x^2+3x\)
C \(8x^2-24x\)
D \(x^2+3x+8\)
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Correct Answer
B. \(8-x^2+3x\)
Explanation
Simple Explanation
((f-g)(x)=8-\(x^2-3x\)=8-x-2 +3x)। घटाने में पूरे (g(x)) के चिह्न बदलते हैं। / ((f-g)(x)=8-\(x^2-3x\)=8-x-2 +3x). In subtraction, signs of the whole (g(x)) change.
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यदि (f(x)=x-2 -25) और (g(x)=x+5), तो (\left\(\frac{f}{g}\right\)(x)) का सरल रूप क्या है, जहाँ \(x\neq-5\)?
If (f(x)=x-2 -25) and (g(x)=x+5), what is the simplified form of (\left\(\frac{f}{g}\right\)(x)), where \(x\neq-5\)?
#algebra
#real functions
#quotient
#factorization
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A (x-5)
B (x+5)
C \(x^2-5\)
D (x-25)
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Explanation
Simple Explanation
(\frac{x-2 -25}{x+5}=\frac{(x-5)(x+5)}{x+5}=x-5)। शर्त \(x\neq-5\) साथ रखें। / (\frac{x-2 -25}{x+5}=\frac{(x-5)(x+5)}{x+5}=x-5). Keep the condition \(x\neq-5\).
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यदि (f(x)=x-2 -4x+4) और (g(x)=x-2), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq2\)?
If (f(x)=x-2 -4x+4) and (g(x)=x-2), what is (\left\(\frac{f}{g}\right\)(x)), where \(x\neq2\)?
#algebra
#real functions
#quotient
#perfect square
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A (x+2)
B (x-2)
C \(x^2-2\)
D (2x-4)
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Explanation
Simple Explanation
क्योंकि (x-2 -4x+4=(x-2)2 ), इसलिए भागफल (x-2) है। (x=2) को डोमेन से हटाएँ। / Since (x-2 -4x+4=(x-2)2 ), the quotient is (x-2). Remove (x=2) from the domain.
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यदि (f(x)=x-1) और (g(x)=x+10), तो ((f+g)(1)) क्या होगा?
If (f(x)=x-1) and (g(x)=x+10), what will ((f+g)(1)) be?
#algebra
#real functions
#value
#addition
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A (10)
B (11)
C (12)
D (0)
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Explanation
Simple Explanation
((f+g)(1)=f(1)+g(1)=0+11=11)। शून्य मान को जोड़ में शामिल करें। / ((f+g)(1)=f(1)+g(1)=0+11=11). Include the zero value in the sum.
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यदि (f(x)=5x) और (g(x)=x+1), तो ((fg)(3)) का मान क्या है?
If (f(x)=5x) and (g(x)=x+1), what is the value of ((fg)(3))?
#algebra
#real functions
#product
#value
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A (45)
B (60)
C (15)
D (20)
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Explanation
Simple Explanation
((fg)(3)=f(3)g(3)=15\cdot4=60)। (fg) का अर्थ फलनों का गुणन है। / ((fg)(3)=f(3)g(3)=15\cdot4=60). (fg) means product of functions.
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यदि (f(x)=x-2 -4) और (g(x)=x-2 +4), तो ((f+g)(x)) क्या है?
If (f(x)=x-2 -4) and (g(x)=x-2 +4), what is ((f+g)(x))?
#algebra
#real functions
#polynomial addition
#cancellation
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A \(2x^2\)
B (8)
C \(x^4-16\)
D \(2x^2+8\)
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Correct Answer
A. \(2x^2\)
Explanation
Simple Explanation
((f+g)(x)=x-2 -4+x-2 +4=2x-2 )। विपरीत स्थिर पद कट जाते हैं। / ((f+g)(x)=x-2 -4+x-2 +4=2x-2 ). Opposite constant terms cancel out.
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यदि (f(x)=4x-2 -3) और (g(x)=x-2 +8), तो ((f-g)(x)) क्या होगा?
If (f(x)=4x-2 -3) and (g(x)=x-2 +8), what will ((f-g)(x)) be?
#algebra
#real functions
#subtraction
#polynomial
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A \(5x^2+5\)
B \(3x^2-11\)
C \(3x^2+5\)
D \(5x^2-11\)
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Correct Answer
B. \(3x^2-11\)
Explanation
Simple Explanation
((f-g)(x)=4x-2 -3-\(x^2+8\)=3x-2 -11)। कोष्ठक के बाद स्थिर पदों पर ध्यान दें। / ((f-g)(x)=4x-2 -3-\(x^2+8\)=3x-2 -11). Pay attention to constant terms after brackets.
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यदि (f(x)=x-5) और (g(x)=3), तो ((fg)(x)) क्या है?
If (f(x)=x-5) and (g(x)=3), what is ((fg)(x))?
#algebra
#real functions
#constant function
#product
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A (3x-15)
B (x-2)
C (3x-5)
D \(x^2-15\)
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Correct Answer
A. (3x-15)
Explanation
Simple Explanation
((fg)(x)=(x-5)\cdot3=3x-15)। स्थिर फलन से गुणा में सभी पद गुणित होते हैं। / ((fg)(x)=(x-5)\cdot3=3x-15). Multiplication by a constant function multiplies all terms.
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यदि (f(x)=12x-6) और (g(x)=6), तो (\left\(\frac{f}{g}\right\)(x)) क्या है?
If (f(x)=12x-6) and (g(x)=6), what is (\left\(\frac{f}{g}\right\)(x))?
#algebra
#real functions
#quotient
#constant denominator
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A (2x-1)
B (12x-1)
C (2x-6)
D (72x-36)
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Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(x)=\frac{12x-6}{6}=2x-1)। अंश के हर पद को (6) से भाग दें। / (\left\(\frac{f}{g}\right\)(x)=\frac{12x-6}{6}=2x-1). Divide every numerator term by (6).
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यदि (f(x)=2x-11) और (g(x)=11-2x), तो ((f+g)(x)) क्या होगा?
If (f(x)=2x-11) and (g(x)=11-2x), what will ((f+g)(x)) be?
#algebra
#real functions
#additive inverse
#addition
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A (0)
B (4x-22)
C (22)
D (2x)
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Explanation
Simple Explanation
((f+g)(x)=(2x-11)+(11-2x)=0)। ये दोनों फलन योगात्मक प्रतिलोम हैं। / ((f+g)(x)=(2x-11)+(11-2x)=0). These two functions are additive inverses.
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यदि (f(x)=3x+8) और (g(x)=3x-8), तो ((f-g)(x)) क्या है?
If (f(x)=3x+8) and (g(x)=3x-8), what is ((f-g)(x))?
#algebra
#real functions
#subtraction
#linear functions
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A (6x)
B (16)
C (6x+16)
D (0)
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Explanation
Simple Explanation
((f-g)(x)=3x+8-(3x-8)=16)। (3x) पद कट जाते हैं। / ((f-g)(x)=3x+8-(3x-8)=16). The (3x) terms cancel out.
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यदि (f(x)=x-5 ) और (g(x)=x-2 ), तो ((fg)(x)) क्या है?
If (f(x)=x-5 ) and (g(x)=x-2 ), what is ((fg)(x))?
#algebra
#real functions
#product
#exponents
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A \(x^7\)
B \(x^{10}\)
C \(2x^5\)
D \(x^3\)
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Correct Answer
A. \(x^7\)
Explanation
Simple Explanation
((fg)(x)=x-5 \cdot x-2 =x-7 )। समान आधार में गुणा करते समय घातों को जोड़ें। / ((fg)(x)=x-5 \cdot x-2 =x-7 ). Add powers while multiplying the same base.
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यदि (f(x)=x-6 ) और (g(x)=x-3 ), तो (\left\(\frac{f}{g}\right\)(x)) क्या होगा, जहाँ \(x\neq0\)?
If (f(x)=x-6 ) and (g(x)=x-3 ), what will (\left\(\frac{f}{g}\right\)(x)) be, where \(x\neq0\)?
#algebra
#real functions
#quotient
#exponents
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A \(x^9\)
B \(x^3\)
C \(x^2\)
D (1)
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Correct Answer
B. \(x^3\)
Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(x)=\frac{x-6 }{x-3 }=x-3 ), जहाँ \(x\neq0\)। भाग में समान आधार की घातें घटाएँ। / (\left\(\frac{f}{g}\right\)(x)=\frac{x-6 }{x-3 }=x-3 ), where \(x\neq0\). In division, subtract powers of the same base.
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यदि (f(x)=2x+1) और (g(x)=x-2 +3), दोनों का डोमेन \(\mathbb{R}\) है, तो ((fg)(x)) का डोमेन क्या है?
If (f(x)=2x+1) and (g(x)=x-2 +3), both have domain \(\mathbb{R}\), what is the domain of ((fg)(x))?
#algebra
#real functions
#domain
#product
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A \(\mathbb{R}\)
B \(\mathbb{R}-{0}\)
C ({1,3})
D \(\emptyset\)
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Correct Answer
A. \(\mathbb{R}\)
Explanation
Simple Explanation
दोनों बहुपद पूरे \(\mathbb{R}\) पर परिभाषित हैं, इसलिए गुणनफल का डोमेन \(\mathbb{R}\) है। डोमेन सामान्य मानों का समुच्चय होता है। / Both polynomials are defined on all \(\mathbb{R}\), so the product domain is \(\mathbb{R}\). The domain is the set of common allowed values.
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यदि (f(x)=\sqrt{x}) और (g(x)=x+2), तो ((f+g)(x)) का डोमेन क्या है?
If (f(x)=\sqrt{x}) and (g(x)=x+2), what is the domain of ((f+g)(x))?
#algebra
#real functions
#domain
#radical function
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A \([0,\infty\))
B \(\mathbb{R}\)
C (\(-\infty,0]\)
D \(\mathbb{R}-{0}\)
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Correct Answer
A. \([0,\infty\))
Explanation
Simple Explanation
\(\sqrt{x}\) के लिए \(x\geq0\) चाहिए, इसलिए योग का डोमेन \([0,\infty\)) है। साझा डोमेन लें। / For \(\sqrt{x}\), we need \(x\geq0\), so the domain of the sum is \([0,\infty\)). Take the common domain.
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यदि (f(x)=x+4) और (g(x)=x-2 -9), तो (\left\(\frac{f}{g}\right\)(x)) का डोमेन क्या है?
If (f(x)=x+4) and (g(x)=x-2 -9), what is the domain of (\left\(\frac{f}{g}\right\)(x))?
#algebra
#real functions
#domain
#quotient
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A \(\mathbb{R}-{-3,3}\)
B \(\mathbb{R}\)
C \(\mathbb{R}-{4}\)
D ((-3,3))
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Correct Answer
A. \(\mathbb{R}-{-3,3}\)
Explanation
Simple Explanation
भाग में (g(x)\neq0) चाहिए, और \(x^2-9=0\) से \(x=\pm3\) मिलता है। इसलिए डोमेन \(\mathbb{R}-{-3,3}\) है। / In division, (g(x)\neq0) is needed, and \(x^2-9=0\) gives \(x=\pm3\). So the domain is \(\mathbb{R}-{-3,3}\).
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यदि (f(x)=x-2 -4) और (g(x)=x-2) हों, तो (\left\(\frac{f}{g}\right\)(x)) का सरल रूप क्या है, जहाँ \(x\ne 2\)?
If (f(x)=x-2 -4) and (g(x)=x-2), what is the simplified form of (\left\(\frac{f}{g}\right\)(x)), where \(x\ne 2\)?
#relations-functions
#algebra-real-functions
#function-quotient
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A (x+2)
B (x-2)
C \(x^2+4\)
D (2x)
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Explanation
Simple Explanation
(\frac{x-2 -4}{x-2}=\frac{(x-2)(x+2)}{x-2}=x+2), पर \(x\ne 2\)। सरल करने के बाद भी मूल हर की शर्त याद रखें। / (\frac{x-2 -4}{x-2}=\frac{(x-2)(x+2)}{x-2}=x+2), but \(x\ne 2\). Keep the original denominator restriction even after simplification.
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यदि (f(x)=2x-3) हो, तो ((3f)(x)) क्या होगा?
If (f(x)=2x-3), what is ((3f)(x))?
#relations-functions
#algebra-real-functions
#scalar-multiple
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A (6x-9)
B (5x-3)
C (6x-3)
D (2x-9)
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Explanation
Simple Explanation
((3f)(x)=3f(x)=3(2x-3)=6x-9)। स्थिर गुणक को सभी पदों से गुणा करें। / ((3f)(x)=3f(x)=3(2x-3)=6x-9). Multiply the constant by every term.
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यदि (f(x)=7-x) और (g(x)=x+1) हों, तो ((f-g)(3)) कितना होगा?
If (f(x)=7-x) and (g(x)=x+1), what is ((f-g)(3))?
#relations-functions
#algebra-real-functions
#function-value
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A (0)
B (4)
C (6)
D (-2)
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Explanation
Simple Explanation
(f(3)=4) और (g(3)=4), इसलिए ((f-g)(3)=0)। मान निकालते समय दोनों फलनों में वही (x) रखें। / (f(3)=4) and (g(3)=4), so ((f-g)(3)=0). Substitute the same (x)-value in both functions.
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यदि (f(x)=x+3) और (g(x)=2x) हों, तो ((fg)(1)) का मान ज्ञात करें।
If (f(x)=x+3) and (g(x)=2x), find the value of ((fg)(1)).
#relations-functions
#algebra-real-functions
#function-product-value
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A (8)
B (6)
C (4)
D (10)
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Explanation
Simple Explanation
(f(1)=4) और (g(1)=2), इसलिए ((fg)(1)=4\cdot 2=8)। गुणन में फलनों के मानों को गुणा करें। / (f(1)=4) and (g(1)=2), so ((fg)(1)=4\cdot 2=8). For products, multiply the function values.
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यदि (f(x)=6x) और (g(x)=3x) हों, तो (\left\(\frac{f}{g}\right\)(2)) क्या होगा?
If (f(x)=6x) and (g(x)=3x), what is (\left\(\frac{f}{g}\right\)(2))?
#relations-functions
#algebra-real-functions
#function-quotient-value
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A (2)
B (3)
C (4)
D (6)
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Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(2)=\frac{f(2)}{g(2)}=\frac{12}{6}=2)। हर का मान (0) नहीं होना चाहिए। / (\left\(\frac{f}{g}\right\)(2)=\frac{f(2)}{g(2)}=\frac{12}{6}=2). The denominator value must not be (0).
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यदि (f(x)=x-2 +1) और (g(x)=x) हों, तो ((f+g)(-1)) का मान क्या है?
If (f(x)=x-2 +1) and (g(x)=x), what is the value of ((f+g)(-1))?
#relations-functions
#algebra-real-functions
#negative-input
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A (1)
B (0)
C (2)
D (-1)
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Explanation
Simple Explanation
(f(-1)=2) और (g(-1)=-1), इसलिए योग (1) है। ऋणात्मक संख्या का वर्ग धनात्मक होता है। / (f(-1)=2) and (g(-1)=-1), so the sum is (1). The square of a negative number is positive.
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यदि (f(x)=x+5) और (g(x)=2) हों, तो ((fg)(x)) क्या होगा?
If (f(x)=x+5) and (g(x)=2), what is ((fg)(x))?
#relations-functions
#algebra-real-functions
#constant-function
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A (2x+10)
B (x+7)
C (2x+5)
D \(x^2+10\)
Explanation opens after your attempt
Correct Answer
A. (2x+10)
Explanation
Simple Explanation
((fg)(x)=(x+5)\cdot 2=2x+10)। स्थिर फलन से गुणा करते समय वितरण नियम लगाएं। / ((fg)(x)=(x+5)\cdot 2=2x+10). Use the distributive law when multiplying by a constant function.
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यदि (f(x)=4x+1) और (g(x)=x-2) हों, तो ((f+g)(x)) में (x) का गुणांक क्या है?
If (f(x)=4x+1) and (g(x)=x-2), what is the coefficient of (x) in ((f+g)(x))?
#relations-functions
#algebra-real-functions
#coefficient
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A (5)
B (4)
C (3)
D (-1)
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Explanation
Simple Explanation
((f+g)(x)=5x-1), इसलिए (x) का गुणांक (5) है। पहले समान पदों को जोड़कर सरल करें। / ((f+g)(x)=5x-1), so the coefficient of (x) is (5). Simplify by combining like terms first.
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यदि (f(x)=x-4) और (g(x)=x+4) हों, तो ((fg)(x)) का सही विस्तार कौन सा है?
If (f(x)=x-4) and (g(x)=x+4), which is the correct expansion of ((fg)(x))?
#relations-functions
#algebra-real-functions
#identity
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A \(x^2-16\)
B \(x^2+16\)
C \(x^2+8x+16\)
D (2x)
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Correct Answer
A. \(x^2-16\)
Explanation
Simple Explanation
((x-4)(x+4)=x-2 -16)। ((a-b)(a+b)=a-2 -b-2 ) को पहचानें। / ((x-4)(x+4)=x-2 -16). Identify ((a-b)(a+b)=a-2 -b-2 ).
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यदि (f(x)=\frac{1}{x}) और (g(x)=x) हों, तो ((fg)(x)) का मान क्या है, जहाँ \(x\ne 0\)?
If (f(x)=\frac{1}{x}) and (g(x)=x), what is ((fg)(x)), where \(x\ne 0\)?
#relations-functions
#algebra-real-functions
#domain-product
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A (1)
B \(x^2\)
C \(\frac{1}{x^2}\)
D (0)
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Explanation
Simple Explanation
((fg)(x)=\frac{1}{x}\cdot x=1), लेकिन \(x\ne 0\)। हर में (x) हो तो शून्य को हटाएं। / ((fg)(x)=\frac{1}{x}\cdot x=1), but \(x\ne 0\). Exclude zero when (x) is in the denominator.
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यदि (f(x)=\sqrt{x}) और (g(x)=x+1) हों, तो ((f+g)(x)) का वास्तविक डोमेन क्या है?
If (f(x)=\sqrt{x}) and (g(x)=x+1), what is the real domain of ((f+g)(x))?
#relations-functions
#algebra-real-functions
#domain-sum
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A \([0,\infty\))
B \(\mathbb{R}\)
C (\(-\infty,0\))
D (\(0,\infty\))
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Correct Answer
A. \([0,\infty\))
Explanation
Simple Explanation
\(\sqrt{x}\) के लिए \(x\ge 0\) चाहिए और (x+1) सभी वास्तविक (x) पर परिभाषित है। अतः डोमेन \([0,\infty\)) है। / For \(\sqrt{x}\), we need \(x\ge 0\), while (x+1) is defined for all real (x). Hence the domain is \([0,\infty\)).
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यदि (f(x)=\frac{1}{x-3}) और (g(x)=x-2 ) हों, तो ((f+g)(x)) का डोमेन क्या होगा?
If (f(x)=\frac{1}{x-3}) and (g(x)=x-2 ), what is the domain of ((f+g)(x))?
#relations-functions
#algebra-real-functions
#domain-restriction
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A \(\mathbb{R}-{3}\)
B \(\mathbb{R}\)
C \(\mathbb{R}-{0}\)
D ({3})
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Correct Answer
A. \(\mathbb{R}-{3}\)
Explanation
Simple Explanation
\(\frac{1}{x-3}\) में (x=3) पर हर (0) हो जाता है। इसलिए योग का डोमेन \(\mathbb{R}-{3}\) है। / In \(\frac{1}{x-3}\), the denominator becomes (0) at (x=3). So the domain of the sum is \(\mathbb{R}-{3}\).
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यदि (f(x)=x+2) और (g(x)=x-5) हों, तो (\left\(\frac{f}{g}\right\)(x)) का डोमेन क्या है?
If (f(x)=x+2) and (g(x)=x-5), what is the domain of (\left\(\frac{f}{g}\right\)(x))?
#relations-functions
#algebra-real-functions
#quotient-domain
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A \(\mathbb{R}-{5}\)
B \(\mathbb{R}-{-2}\)
C \(\mathbb{R}\)
D ({5})
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{5}\)
Explanation
Simple Explanation
भागफल में (g(x)\ne 0) होना चाहिए। (x-5=0) से (x=5), इसलिए (5) हटेगा। / For a quotient, (g(x)\ne 0) is required. Since (x-5=0) gives (x=5), exclude (5).
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यदि (f(x)=x-2 +3) और (g(x)=2x-1) हों, तो ((2f+g)(x)) क्या है?
If (f(x)=x-2 +3) and (g(x)=2x-1), what is ((2f+g)(x))?
#relations-functions
#algebra-real-functions
#linear-combination
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A \(2x^2+2x+5\)
B \(2x^2+2x+2\)
C \(x^2+2x+5\)
D \(2x^2-2x+5\)
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Correct Answer
A. \(2x^2+2x+5\)
Explanation
Simple Explanation
((2f+g)(x)=2\(x^2+3\)+(2x-1)=2x-2 +2x+5)। पहले गुणा करें फिर जोड़ें। / ((2f+g)(x)=2\(x^2+3\)+(2x-1)=2x-2 +2x+5). Multiply first and then add.
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यदि (f(x)=3x+2) और (g(x)=x-2 ) हों, तो ((f+2g)(1)) का मान क्या है?
If (f(x)=3x+2) and (g(x)=x-2 ), what is the value of ((f+2g)(1))?
#relations-functions
#algebra-real-functions
#combined-value
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A (7)
B (5)
C (9)
D (3)
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Explanation
Simple Explanation
(f(1)=5) और (g(1)=1), इसलिए (f(1)+2g(1)=7)। संयुक्त फलन में गुणक को न भूलें। / (f(1)=5) and (g(1)=1), so (f(1)+2g(1)=7). Do not forget the multiplier in a combined function.
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यदि (f(x)=x) और (g(x)=x-2 ) हों, तो ((f+g)(x)) किसके बराबर है?
If (f(x)=x) and (g(x)=x-2 ), then ((f+g)(x)) is equal to which expression?
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#common-mistake
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A \(x+x^2\)
B \(x^3\)
C \(2x^2\)
D \(x^2-x\)
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Correct Answer
A. \(x+x^2\)
Explanation
Simple Explanation
योग में फलनों के मान जोड़े जाते हैं, गुणा नहीं किए जाते। अतः ((f+g)(x)=x+x-2 )। / In addition, function values are added, not multiplied. Hence ((f+g)(x)=x+x-2 ).
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यदि (f(x)=2x) और (g(x)=x+3) हों, तो ((f-g)(0)) क्या है?
If (f(x)=2x) and (g(x)=x+3), what is ((f-g)(0))?
#relations-functions
#algebra-real-functions
#zero-input
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A (-3)
B (3)
C (0)
D (6)
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Explanation
Simple Explanation
(f(0)=0) और (g(0)=3), इसलिए ((f-g)(0)=0-3=-3)। (x=0) रखने पर स्थिर पद बचता है। / (f(0)=0) and (g(0)=3), so ((f-g)(0)=0-3=-3). At (x=0), the constant term remains.
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यदि (f(x)=x-2 -1) और (g(x)=x+1) हों, तो (\left\(\frac{f}{g}\right\)(0)) का मान क्या है?
If (f(x)=x-2 -1) and (g(x)=x+1), what is the value of (\left\(\frac{f}{g}\right\)(0))?
#relations-functions
#algebra-real-functions
#quotient-value
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A (-1)
B (1)
C (0)
D अपरिभाषित / Undefined
Explanation opens after your attempt
Explanation
Simple Explanation
(f(0)=-1) और (g(0)=1), इसलिए भागफल (-1) है। केवल तब अपरिभाषित होगा जब हर (0) हो। / (f(0)=-1) and (g(0)=1), so the quotient is (-1). It is undefined only when the denominator is (0).
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यदि (f(x)=x+6) और (g(x)=x-6) हों, तो ((f+g)(x)) क्या होगा?
If (f(x)=x+6) and (g(x)=x-6), what is ((f+g)(x))?
#relations-functions
#algebra-real-functions
#simplification
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A (2x)
B \(x^2-36\)
C (12)
D (0)
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Explanation
Simple Explanation
((x+6)+(x-6)=2x) क्योंकि (6) और (-6) कट जाते हैं। संकेतों पर ध्यान देना आसान अंक दिलाता है। / ((x+6)+(x-6)=2x) because (6) and (-6) cancel. Careful signs can earn easy marks.
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यदि (f(x)=2x+1) और (g(x)=x+2) हों, तो ((fg)(0)) कितना है?
If (f(x)=2x+1) and (g(x)=x+2), what is ((fg)(0))?
#relations-functions
#algebra-real-functions
#evaluation
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A (2)
B (0)
C (1)
D (3)
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Explanation
Simple Explanation
(f(0)=1) और (g(0)=2), इसलिए ((fg)(0)=2)। पहले अलग-अलग मान निकालना सुरक्षित तरीका है। / (f(0)=1) and (g(0)=2), so ((fg)(0)=2). Finding values separately is a safe method.
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यदि (f(x)=x-2 ) और (g(x)=2x) हों, तो ((f-g)(2)) क्या होगा?
If (f(x)=x-2 ) and (g(x)=2x), what is ((f-g)(2))?
#relations-functions
#algebra-real-functions
#value-comparison
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A (0)
B (4)
C (8)
D (-4)
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Explanation
Simple Explanation
(f(2)=4) और (g(2)=4), इसलिए अंतर (0) है। समान मान मिलने पर घटाव शून्य होगा। / (f(2)=4) and (g(2)=4), so the difference is (0). If the values are equal, their difference is zero.
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यदि (f(x)=\sqrt{x-1}) और (g(x)=x) हों, तो ((fg)(x)) का वास्तविक डोमेन क्या है?
If (f(x)=\sqrt{x-1}) and (g(x)=x), what is the real domain of ((fg)(x))?
#relations-functions
#algebra-real-functions
#domain-product
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A \([1,\infty\))
B \([0,\infty\))
C \(\mathbb{R}\)
D (\(-\infty,1]\)
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Correct Answer
A. \([1,\infty\))
Explanation
Simple Explanation
\(\sqrt{x-1}\) के लिए \(x-1\ge 0\), यानी \(x\ge 1\)। गुणन का डोमेन दोनों डोमेन का प्रतिच्छेद होता है। / For \(\sqrt{x-1}\), \(x-1\ge 0\), so \(x\ge 1\). The product domain is the intersection of both domains.
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यदि (f(x)=x+1) और (g(x)=\frac{1}{x}) हों, तो ((f+g)(x)) का डोमेन क्या है?
If (f(x)=x+1) and (g(x)=\frac{1}{x}), what is the domain of ((f+g)(x))?
#relations-functions
#algebra-real-functions
#domain-sum
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A \(\mathbb{R}-{0}\)
B \(\mathbb{R}\)
C (\(0,\infty\))
D ({0})
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{0}\)
Explanation
Simple Explanation
\(\frac{1}{x}\) में (x=0) मान्य नहीं है। इसलिए योग का डोमेन \(\mathbb{R}-{0}\) है। / In \(\frac{1}{x}\), (x=0) is not allowed. Therefore the domain of the sum is \(\mathbb{R}-{0}\).
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यदि (f(x)=\frac{x}{x+2}) और (g(x)=x-1) हों, तो ((fg)(x)) के डोमेन से कौन सा मान हटेगा?
If (f(x)=\frac{x}{x+2}) and (g(x)=x-1), which value is excluded from the domain of ((fg)(x))?
#relations-functions
#algebra-real-functions
#excluded-value
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A (-2)
B (2)
C (1)
D (0)
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Explanation
Simple Explanation
(x+2=0) से (x=-2) पर (f(x)) अपरिभाषित है। गुणन में भी यह मान हटेगा। / Since (x+2=0) gives (x=-2), (f(x)) is undefined there. This value is also excluded in the product.
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यदि (f(x)=2x-2 ) और (g(x)=x-2 +3) हों, तो ((f+g)(x)) क्या है?
If (f(x)=2x-2 ) and (g(x)=x-2 +3), what is ((f+g)(x))?
#relations-functions
#algebra-real-functions
#quadratic-sum
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A \(3x^2+3\)
B \(2x^4+6x^2\)
C \(x^2+3\)
D \(3x^4\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+3\)
Explanation
Simple Explanation
((f+g)(x)=2x-2 +\(x^2+3\)=3x-2 +3)। समान घात वाले पद ही जोड़े जाते हैं। / ((f+g)(x)=2x-2 +\(x^2+3\)=3x-2 +3). Only terms with the same power are combined.
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यदि (f(x)=x-2 +5) और (g(x)=x-2 -2) हों, तो ((f-g)(x)) क्या होगा?
If (f(x)=x-2 +5) and (g(x)=x-2 -2), what is ((f-g)(x))?
#relations-functions
#algebra-real-functions
#subtraction-signs
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A (7)
B \(2x^2+3\)
C (3)
D \(x^2+7\)
Explanation opens after your attempt
Explanation
Simple Explanation
(\(x^2+5\)-\(x^2-2\)=7)। दूसरे कोष्ठक के दोनों पदों के चिह्न बदलते हैं। / (\(x^2+5\)-\(x^2-2\)=7). Both signs inside the second bracket change.
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यदि (f(x)=x+2) और (g(x)=x+3) हों, तो ((fg)(x)) में स्थिर पद क्या है?
If (f(x)=x+2) and (g(x)=x+3), what is the constant term in ((fg)(x))?
#relations-functions
#algebra-real-functions
#constant-term
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A (6)
B (5)
C (2)
D (3)
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Explanation
Simple Explanation
((x+2)(x+3)=x-2 +5x+6), इसलिए स्थिर पद (6) है। स्थिर पद अक्सर स्थिरों के गुणन से मिलता है। / ((x+2)(x+3)=x-2 +5x+6), so the constant term is (6). The constant term often comes from multiplying constants.
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यदि (f(x)=4) और (g(x)=x-2 -1) हों, तो ((f-g)(x)) क्या है?
If (f(x)=4) and (g(x)=x-2 -1), what is ((f-g)(x))?
#relations-functions
#algebra-real-functions
#constant-minus-function
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A \(5-x^2\)
B \(x^2+3\)
C \(4x^2-4\)
D \(x^2-5\)
Explanation opens after your attempt
Correct Answer
A. \(5-x^2\)
Explanation
Simple Explanation
((f-g)(x)=4-\(x^2-1\)=5-x-2 )। कोष्ठक हटाते समय ऋण चिह्न का ध्यान रखें। / ((f-g)(x)=4-\(x^2-1\)=5-x-2 ). Watch the minus sign while removing brackets.
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यदि (f(x)=x-1) और (g(x)=3x+2) हों, तो ((g-f)(x)) क्या होगा?
If (f(x)=x-1) and (g(x)=3x+2), what is ((g-f)(x))?
#relations-functions
#algebra-real-functions
#order-of-subtraction
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A (2x+3)
B (4x+1)
C (2x+1)
D \(3x^2-x-2\)
Explanation opens after your attempt
Explanation
Simple Explanation
((g-f)(x)=g(x)-f(x)=(3x+2)-(x-1)=2x+3)। क्रम बदलने से अंतर बदल सकता है। / ((g-f)(x)=g(x)-f(x)=(3x+2)-(x-1)=2x+3). Changing the order can change the difference.
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यदि (f(x)=x-2 ) और (g(x)=x) हों, तो ((f-g)(-2)) का मान क्या है?
If (f(x)=x-2 ) and (g(x)=x), what is the value of ((f-g)(-2))?
#relations-functions
#algebra-real-functions
#negative-value
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A (6)
B (2)
C (4)
D (-6)
Explanation opens after your attempt
Explanation
Simple Explanation
(f(-2)=4) और (g(-2)=-2), इसलिए (4-(-2)=6)। ऋणात्मक संख्या घटाते समय जोड़ बनता है। / (f(-2)=4) and (g(-2)=-2), so (4-(-2)=6). Subtracting a negative number becomes addition.
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यदि (f(x)=x+1), (g(x)=x+2) और (h(x)=x+3) हों, तो ((f+g+h)(x)) क्या है?
If (f(x)=x+1), (g(x)=x+2), and (h(x)=x+3), what is ((f+g+h)(x))?
#relations-functions
#algebra-real-functions
#three-functions
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A (3x+6)
B (x+6)
C (3x+3)
D \(x^3+6\)
Explanation opens after your attempt
Explanation
Simple Explanation
तीनों फलनों को जोड़ने पर (x+x+x=3x) और (1+2+3=6)। इसलिए उत्तर (3x+6) है। / Adding the three functions gives (x+x+x=3x) and (1+2+3=6). So the answer is (3x+6).
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यदि (f(x)=2x+5) और (g(x)=x) हों, तो (\left\(\frac{f}{g}\right\)(1)) क्या होगा?
If (f(x)=2x+5) and (g(x)=x), what is (\left\(\frac{f}{g}\right\)(1))?
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#quotient-evaluation
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A (7)
B (5)
C (2)
D (3)
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Explanation
Simple Explanation
(\left\(\frac{f}{g}\right\)(1)=\frac{f(1)}{g(1)}=\frac{7}{1}=7)। भागफल में हर का मान जांचना जरूरी है। / (\left\(\frac{f}{g}\right\)(1)=\frac{f(1)}{g(1)}=\frac{7}{1}=7). Always check the denominator value in a quotient.
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यदि (f(x)=x-2 -9) और (g(x)=x+3) हों, तो (\left\(\frac{f}{g}\right\)(x)) का सरल रूप क्या है, जहाँ \(x\ne -3\)?
If (f(x)=x-2 -9) and (g(x)=x+3), what is the simplified form of (\left\(\frac{f}{g}\right\)(x)), where \(x\ne -3\)?
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#algebra-real-functions
#simplified-quotient
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A (x-3)
B (x+3)
C \(x^2+9\)
D (2x)
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Explanation
Simple Explanation
(\frac{x-2 -9}{x+3}=\frac{(x-3)(x+3)}{x+3}=x-3)। शर्त \(x\ne -3\) मूल हर से आती है। / (\frac{x-2 -9}{x+3}=\frac{(x-3)(x+3)}{x+3}=x-3). The condition \(x\ne -3\) comes from the original denominator.
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यदि (f(x)=\frac{1}{x-1}) और (g(x)=\frac{1}{x+1}) हों, तो ((f+g)(x)) के डोमेन से कौन से मान हटेंगे?
If (f(x)=\frac{1}{x-1}) and (g(x)=\frac{1}{x+1}), which values are excluded from the domain of ((f+g)(x))?
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#multiple-restrictions
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A (1,-1)
B (0,1)
C (1,2)
D केवल (0) / Only (0)
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Explanation
Simple Explanation
(x-1=0) से (x=1) और (x+1=0) से (x=-1)। योग के डोमेन में दोनों प्रतिबंध लागू होंगे। / (x-1=0) gives (x=1), and (x+1=0) gives (x=-1). Both restrictions apply to the domain of the sum.
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यदि (f(x)=x+4) और (g(x)=2x-3) हों, तो ((f+g)(5)) का मान क्या है?
If (f(x)=x+4) and (g(x)=2x-3), what is the value of ((f+g)(5))?
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#easy-numerical
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A (16)
B (14)
C (18)
D (10)
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Explanation
Simple Explanation
(f(5)=9) और (g(5)=7), इसलिए योग (16) है। सीधे ((f+g)(x)=3x+1) बनाकर भी मान मिल सकता है। / (f(5)=9) and (g(5)=7), so the sum is (16). You can also form ((f+g)(x)=3x+1) first.
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यदि (f(x)=3x-2) और (g(x)=x+5) हों, तो ((fg)(2)) का मान क्या है?
If (f(x)=3x-2) and (g(x)=x+5), what is the value of ((fg)(2))?
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A (28)
B (14)
C (21)
D (35)
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Explanation
Simple Explanation
(f(2)=4) और (g(2)=7), इसलिए ((fg)(2)=28)। उत्पाद में जोड़ नहीं, गुणा करें। / (f(2)=4) and (g(2)=7), so ((fg)(2)=28). For a product, multiply, do not add.
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यदि (f(x)=x-2 +2) और (g(x)=2x) हों, तो ((f+g)(x)) किस पूर्ण वर्ग जैसा लिखा जा सकता है?
If (f(x)=x-2 +2) and (g(x)=2x), which completed-square-like form represents ((f+g)(x))?
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#completed-square
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A ((x+1)2 +1)
B ((x-1)2 +1)
C ((x+2)2 )
D ((x+1)2 -1)
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Correct Answer
A. ((x+1)2 +1)
Explanation
Simple Explanation
((f+g)(x)=x-2 +2x+2=(x+1)2 +1)। पूर्ण वर्ग पहचानना ग्राफ और रेंज में भी मदद करता है। / ((f+g)(x)=x-2 +2x+2=(x+1)2 +1). Recognizing a completed square also helps in graphs and range.
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यदि (f(x)=x-2) और (g(x)=x-2) हों, तो ((f-g)(x)) क्या होगा?
If (f(x)=x-2) and (g(x)=x-2), what is ((f-g)(x))?
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A (0)
B (2x-4)
C \(x^2-4x+4\)
D (x-2)
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Explanation
Simple Explanation
दोनों फलन समान हैं, इसलिए उनका अंतर हर (x) पर (0) है। समान फलनों का अंतर शून्य फलन होता है। / The two functions are identical, so their difference is (0) for every (x). The difference of identical functions is the zero function.
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यदि (f(x)=1) और (g(x)=x-2 +2x) हों, तो ((fg)(x)) क्या है?
If (f(x)=1) and (g(x)=x-2 +2x), what is ((fg)(x))?
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A \(x^2+2x\)
B \(x^2+2x+1\)
C (1)
D \(x^2\)
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Correct Answer
A. \(x^2+2x\)
Explanation
Simple Explanation
(1) से गुणा करने पर फलन नहीं बदलता। इसलिए ((fg)(x)=x-2 +2x) है। / Multiplying by (1) does not change the function. Therefore ((fg)(x)=x-2 +2x).
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यदि (f(x)=0) और (g(x)=x+7) हों, तो ((f+g)(x)) क्या है?
If (f(x)=0) and (g(x)=x+7), what is ((f+g)(x))?
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#zero-function-addition
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A (x+7)
B (0)
C (7x)
D (x)
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Explanation
Simple Explanation
शून्य फलन जोड़ने से दूसरा फलन वैसा ही रहता है। इसलिए ((f+g)(x)=x+7)। / Adding the zero function leaves the other function unchanged. Hence ((f+g)(x)=x+7).
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यदि (f(x)=x-2 -2x) और (g(x)=x) हों, तो ((f+3g)(x)) क्या होगा?
If (f(x)=x-2 -2x) and (g(x)=x), what is ((f+3g)(x))?
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A \(x^2+x\)
B \(x^2-5x\)
C \(3x^2+x\)
D \(x^2+3\)
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Correct Answer
A. \(x^2+x\)
Explanation
Simple Explanation
((f+3g)(x)=x-2 -2x+3x=x-2 +x)। रैखिक संयोजन में गुणक सही लगाएं। / ((f+3g)(x)=x-2 -2x+3x=x-2 +x). Apply the multiplier correctly in a linear combination.
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यदि (f(x)=\frac{1}{x+4}) और (g(x)=x-2 ) हों, तो ((f-g)(x)) का डोमेन क्या है?
If (f(x)=\frac{1}{x+4}) and (g(x)=x-2 ), what is the domain of ((f-g)(x))?
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#domain-difference
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A \(\mathbb{R}-{-4}\)
B \(\mathbb{R}-{4}\)
C \(\mathbb{R}\)
D (\(4,\infty\))
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Correct Answer
A. \(\mathbb{R}-{-4}\)
Explanation
Simple Explanation
\(\frac{1}{x+4}\) में (x=-4) पर हर (0) है। अंतर का डोमेन भी \(\mathbb{R}-{-4}\) होगा। / In \(\frac{1}{x+4}\), the denominator is (0) at (x=-4). The domain of the difference is also \(\mathbb{R}-{-4}\).
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यदि (f(x)=x+1) और (g(x)=x-2 +1) हों, तो (\left\(\frac{g}{f}\right\)(x)) का डोमेन क्या है?
If (f(x)=x+1) and (g(x)=x-2 +1), what is the domain of (\left\(\frac{g}{f}\right\)(x))?
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#quotient-domain
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A \(\mathbb{R}-{-1}\)
B \(\mathbb{R}-{1}\)
C \(\mathbb{R}\)
D (\(-\infty,-1\))
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Correct Answer
A. \(\mathbb{R}-{-1}\)
Explanation
Simple Explanation
\(\frac{g}{f}\) में हर (f(x)=x+1) है, इसलिए (x=-1) हटेगा। भागफल में हर वाले फलन को ध्यान से देखें। / In \(\frac{g}{f}\), the denominator is (f(x)=x+1), so (x=-1) is excluded. Identify the denominator function carefully.
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यदि (f(x)=2x+3) और (g(x)=2x-3) हों, तो ((fg)(x)) क्या है?
If (f(x)=2x+3) and (g(x)=2x-3), what is ((fg)(x))?
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#algebra-real-functions
#product-identity
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A \(4x^2-9\)
B \(4x^2+9\)
C \(2x^2-9\)
D (4x-9)
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Correct Answer
A. \(4x^2-9\)
Explanation
Simple Explanation
((2x+3)(2x-3)=(2x)2 -32 =4x-2 -9)। यह अंतर वर्ग का सीधा प्रयोग है। / ((2x+3)(2x-3)=(2x)2 -32 =4x-2 -9). This is a direct use of difference of squares.
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यदि (f(x)=x-2 +1) और (g(x)=x-2 +1) हों, तो (\left\(\frac{f}{g}\right\)(x)) किसके बराबर है?
If (f(x)=x-2 +1) and (g(x)=x-2 +1), then (\left\(\frac{f}{g}\right\)(x)) equals which expression?
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A (1)
B (0)
C \(x^2+1\)
D \(2x^2+2\)
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Explanation
Simple Explanation
क्योंकि (f(x)=g(x)), इसलिए (\frac{f(x)}{g(x)}=1)। यहाँ \(x^2+1\) कभी (0) नहीं होता, इसलिए सभी वास्तविक (x) मान्य हैं। / Since (f(x)=g(x)), (\frac{f(x)}{g(x)}=1). Here \(x^2+1\) is never (0), so all real (x) are valid.
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यदि (f(x)=x-2 +4x) और (g(x)=2x-2 -x) हों, तो ((f+g)(x)) क्या है?
If (f(x)=x-2 +4x) and (g(x)=2x-2 -x), what is ((f+g)(x))?
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A \(3x^2+3x\)
B \(x^2+5x\)
C \(3x^2-3x\)
D \(2x^4-4x^2\)
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Correct Answer
A. \(3x^2+3x\)
Explanation
Simple Explanation
((f+g)(x)=x-2 +4x+2x-2 -x=3x-2 +3x)। समान घात वाले पदों को ही जोड़ें। / ((f+g)(x)=x-2 +4x+2x-2 -x=3x-2 +3x). Add only like terms with the same power.
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यदि (f(x)=5x+2) और (g(x)=2x-7) हों, तो ((f-g)(1)) का मान क्या होगा?
If (f(x)=5x+2) and (g(x)=2x-7), what is the value of ((f-g)(1))?
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#function-subtraction
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A (12)
B (7)
C (9)
D (4)
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Explanation
Simple Explanation
(f(1)=7) और (g(1)=-5), इसलिए ((f-g)(1)=7-(-5)=12)। ऋणात्मक मान घटाते समय सावधानी रखें। / (f(1)=7) and (g(1)=-5), so ((f-g)(1)=7-(-5)=12). Be careful while subtracting a negative value.
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यदि (f(x)=x+2) और (g(x)=x-2 -2x) हों, तो ((fg)(2)) क्या है?
If (f(x)=x+2) and (g(x)=x-2 -2x), what is ((fg)(2))?
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A (0)
B (4)
C (8)
D (2)
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Explanation
Simple Explanation
(f(2)=4) और (g(2)=0), इसलिए ((fg)(2)=4\cdot 0=0)। गुणन में किसी एक मान के (0) होने पर उत्पाद (0) होता है। / (f(2)=4) and (g(2)=0), so ((fg)(2)=4\cdot 0=0). In multiplication, if one value is (0), the product is (0).
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यदि (f(x)=\sqrt{x+2}) और (g(x)=\frac{1}{x-1}) हों, तो ((f+g)(x)) का वास्तविक डोमेन क्या है?
If (f(x)=\sqrt{x+2}) and (g(x)=\frac{1}{x-1}), what is the real domain of ((f+g)(x))?
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#domain
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A \([-2,\infty\)-{1})
B \(\mathbb{R}-{1}\)
C \([-2,\infty\))
D (\(1,\infty\))
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Correct Answer
A. \([-2,\infty\)-{1})
Explanation
Simple Explanation
\(\sqrt{x+2}\) के लिए \(x\ge -2\) और \(\frac{1}{x-1}\) के लिए \(x\ne 1\) चाहिए। दोनों शर्तों को साथ लगाएं। / For \(\sqrt{x+2}\), \(x\ge -2\), and for \(\frac{1}{x-1}\), \(x\ne 1\). Apply both conditions together.
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यदि (f(x)=x-2 -1) और (g(x)=x-2 +1) हों, तो ((g-f)(x)) क्या होगा?
If (f(x)=x-2 -1) and (g(x)=x-2 +1), what is ((g-f)(x))?
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#function-difference
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A (2)
B \(2x^2\)
C (0)
D \(x^2+2\)
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Explanation
Simple Explanation
((g-f)(x)=\(x^2+1\)-\(x^2-1\)=2)। घटाते समय दूसरे कोष्ठक के चिह्न बदलते हैं। / ((g-f)(x)=\(x^2+1\)-\(x^2-1\)=2). While subtracting, the signs inside the second bracket change.
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