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)
Explanation opens after your attempt
Step 1
Concept
In addition, like (x) terms are added, so ((f+g)(x)=x+2+3x=4x+2). In exams, open brackets first.
Step 2
Why this answer is correct
The correct answer is A. (4x+2). In addition, like (x) terms are added, so ((f+g)(x)=x+2+3x=4x+2). In exams, open brackets first.
Step 3
Exam Tip
योग में समान (x) पद जोड़े जाते हैं, इसलिए ((f+g)(x)=x+2+3x=4x+2)। परीक्षा में पहले कोष्ठक खोलें।
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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)
Explanation opens after your attempt
Step 1
Concept
((f-g)(x)=(5x-1)-(2x+4)=3x-5). In subtraction, change every sign of the second function.
Step 2
Why this answer is correct
The correct answer is A. (3x-5). ((f-g)(x)=(5x-1)-(2x+4)=3x-5). In subtraction, change every sign of the second function.
Step 3
Exam Tip
((f-g)(x)=(5x-1)-(2x+4)=3x-5)। घटाने में दूसरे फलन के सभी चिह्न बदलें।
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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 \(x^2-2x+1\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-1\)
Step 1
Concept
In multiplication, ((fg)(x)=f(x)g(x)), so ((x+1)(x-1)=x-2 -1). Remember the identity \(a^2-b^2\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-1\). In multiplication, ((fg)(x)=f(x)g(x)), so ((x+1)(x-1)=x-2 -1). Remember the identity \(a^2-b^2\).
Step 3
Exam Tip
गुणन में ((fg)(x)=f(x)g(x)), इसलिए ((x+1)(x-1)=x-2 -1)। पहचान \(a^2-b^2\) याद रखें।
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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)
Explanation opens after your attempt
Step 1
Concept
In division, (\left\(\frac{f}{g}\right\)(x)=\frac{2x+6}{2}=x+3). The denominator must not be zero.
Step 2
Why this answer is correct
The correct answer is A. (x+3). In division, (\left\(\frac{f}{g}\right\)(x)=\frac{2x+6}{2}=x+3). The denominator must not be zero.
Step 3
Exam Tip
भाग में (\left\(\frac{f}{g}\right\)(x)=\frac{2x+6}{2}=x+3)। हर शून्य नहीं होना चाहिए।
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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)
Explanation opens after your attempt
Step 1
Concept
((f+g)(2)=f(2)+g(2)=4+4=8). You may add functions first or substitute directly.
Step 2
Why this answer is correct
The correct answer is A. (8). ((f+g)(2)=f(2)+g(2)=4+4=8). You may add functions first or substitute directly.
Step 3
Exam Tip
((f+g)(2)=f(2)+g(2)=4+4=8)। पहले फलन जोड़ें या सीधे मान रखें।
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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)
Explanation opens after your attempt
Step 1
Concept
((f-g)(1)=f(1)-g(1)=3-6=-3). Check the correct order before substituting.
Step 2
Why this answer is correct
The correct answer is A. (-3). ((f-g)(1)=f(1)-g(1)=3-6=-3). Check the correct order before substituting.
Step 3
Exam Tip
((f-g)(1)=f(1)-g(1)=3-6=-3)। मान रखने से पहले सही क्रम देखें।
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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)
Explanation opens after your attempt
Step 1
Concept
((fg)(1)=f(1)g(1)=3\times4=12). In product of functions, multiply the values.
Step 2
Why this answer is correct
The correct answer is A. (12). ((fg)(1)=f(1)g(1)=3\times4=12). In product of functions, multiply the values.
Step 3
Exam Tip
((fg)(1)=f(1)g(1)=3\times4=12)। गुणन फलन में मानों का गुणा करें।
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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)
Explanation opens after your attempt
Step 1
Concept
(\left\(\frac{f}{g}\right\)(3)=\frac{9-4}{3-2}=5). In division, the denominator value must not be zero.
Step 2
Why this answer is correct
The correct answer is A. (5). (\left\(\frac{f}{g}\right\)(3)=\frac{9-4}{3-2}=5). In division, the denominator value must not be zero.
Step 3
Exam Tip
(\left\(\frac{f}{g}\right\)(3)=\frac{9-4}{3-2}=5)। भाग में हर का मान शून्य नहीं होना चाहिए।
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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 \(x^2+3x\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x+1\)
Step 1
Concept
((f+g)(x)=x-2 +1+2x=x-2 +2x+1). Writing terms in descending powers is a good exam habit.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x+1\). ((f+g)(x)=x-2 +1+2x=x-2 +2x+1). Writing terms in descending powers is a good exam habit.
Step 3
Exam Tip
((f+g)(x)=x-2 +1+2x=x-2 +2x+1)। पदों को घटते घात क्रम में लिखना अच्छा रहता है।
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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)
Explanation opens after your attempt
Correct Answer
A. (3x+10)
Step 1
Concept
((f-g)(x)=(4x+7)-(x-3)=3x+10). Apply the minus sign to the whole bracket.
Step 2
Why this answer is correct
The correct answer is A. (3x+10). ((f-g)(x)=(4x+7)-(x-3)=3x+10). Apply the minus sign to the whole bracket.
Step 3
Exam Tip
((f-g)(x)=(4x+7)-(x-3)=3x+10)। ऋण चिह्न को पूरे कोष्ठक पर लगाएँ।
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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 \(2x+x^2\)
Explanation opens after your attempt
Correct Answer
A. \(2x^3\)
Step 1
Concept
((fg)(x)=2x\cdot x-2 =2x-3 ). For the same base, powers are added in multiplication.
Step 2
Why this answer is correct
The correct answer is A. \(2x^3\). ((fg)(x)=2x\cdot x-2 =2x-3 ). For the same base, powers are added in multiplication.
Step 3
Exam Tip
((fg)(x)=2x\cdot x-2 =2x-3 )। समान आधार में घातें जुड़ती हैं।
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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 \(9x^3\)
Explanation opens after your attempt
Step 1
Concept
(\left\(\frac{f}{g}\right\)(x)=\frac{6x-2 }{3x}=2x), because \(x\neq0\). In quotient questions, check the condition first.
Step 2
Why this answer is correct
The correct answer is A. (2x). (\left\(\frac{f}{g}\right\)(x)=\frac{6x-2 }{3x}=2x), because \(x\neq0\). In quotient questions, check the condition first.
Step 3
Exam Tip
(\left\(\frac{f}{g}\right\)(x)=\frac{6x-2 }{3x}=2x), क्योंकि \(x\neq0\)। भाग में पहले शर्त जाँचें।
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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)
Explanation opens after your attempt
Step 1
Concept
((2f)(x)=2f(x)=2(x+4)=2x+8). In scalar multiplication, multiply every term.
Step 2
Why this answer is correct
The correct answer is A. (2x+8). ((2f)(x)=2f(x)=2(x+4)=2x+8). In scalar multiplication, multiply every term.
Step 3
Exam Tip
((2f)(x)=2f(x)=2(x+4)=2x+8)। स्थिर गुणन में हर पद से गुणा करें।
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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)
Explanation opens after your attempt
Correct Answer
A. (-3x+2)
Step 1
Concept
((-f)(x)=-f(x)=-(3x-2)=-3x+2). The negative sign applies to the whole function.
Step 2
Why this answer is correct
The correct answer is A. (-3x+2). ((-f)(x)=-f(x)=-(3x-2)=-3x+2). The negative sign applies to the whole function.
Step 3
Exam Tip
((-f)(x)=-f(x)=-(3x-2)=-3x+2)। ऋण पूरे फलन पर लगता है।
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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)
Explanation opens after your attempt
Correct Answer
A. \(2x^2\)
Step 1
Concept
((f+f)(x)=x-2 +x-2 =2x-2 ). Add like terms, not the powers.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2\). ((f+f)(x)=x-2 +x-2 =2x-2 ). Add like terms, not the powers.
Step 3
Exam Tip
((f+f)(x)=x-2 +x-2 =2x-2 )। समान पदों को जोड़ें, घातों को नहीं।
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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)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x+1\)
Step 1
Concept
((ff)(x)=f(x)f(x)=(x+1)2 =x-2 +2x+1). Do not confuse ((ff)(x)) with ((f+f)(x)).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x+1\). ((ff)(x)=f(x)f(x)=(x+1)2 =x-2 +2x+1). Do not confuse ((ff)(x)) with ((f+f)(x)).
Step 3
Exam Tip
((ff)(x)=f(x)f(x)=(x+1)2 =x-2 +2x+1)। ((ff)(x)) को ((f+f)(x)) न समझें।
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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)
Explanation opens after your attempt
Step 1
Concept
Both functions are equal, so ((f-g)(x)=(x+5)-(x+5)=0). The difference of equal functions is zero.
Step 2
Why this answer is correct
The correct answer is A. (0). Both functions are equal, so ((f-g)(x)=(x+5)-(x+5)=0). The difference of equal functions is zero.
Step 3
Exam Tip
दोनों फलन समान हैं, इसलिए ((f-g)(x)=(x+5)-(x+5)=0)। समान फलनों का अंतर शून्य होता है।
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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 \(3x^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3\)
Step 1
Concept
Adding the zero function does not change the function, so ((f+g)(x)=x-2 +3). This is the identity property of addition.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3\). Adding the zero function does not change the function, so ((f+g)(x)=x-2 +3). This is the identity property of addition.
Step 3
Exam Tip
शून्य फलन जोड़ने से फलन नहीं बदलता, इसलिए ((f+g)(x)=x-2 +3)। यह योग का पहचान गुण है।
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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 \(x^2+2x\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-2x\)
Step 1
Concept
Multiplying by the unit function (1) gives ((fg)(x)=g(x)). In multiplication, (1) is the identity element.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-2x\). Multiplying by the unit function (1) gives ((fg)(x)=g(x)). In multiplication, (1) is the identity element.
Step 3
Exam Tip
एकक फलन (1) से गुणा करने पर ((fg)(x)=g(x)) रहता है। गुणन में (1) पहचान तत्व है।
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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)
Explanation opens after your attempt
Step 1
Concept
((f+g)(x)=(x-2)+(x+2)=2x). Opposite constant terms cancel out.
Step 2
Why this answer is correct
The correct answer is A. (2x). ((f+g)(x)=(x-2)+(x+2)=2x). Opposite constant terms cancel out.
Step 3
Exam Tip
((f+g)(x)=(x-2)+(x+2)=2x)। विपरीत स्थिर पद कट जाते हैं।
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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 \(x^2+3x\)
Explanation opens after your attempt
Step 1
Concept
((f-g)(x)=x-2 +2x-\(x^2-x\)=3x). The like \(x^2\) terms cancel out.
Step 2
Why this answer is correct
The correct answer is A. (3x). ((f-g)(x)=x-2 +2x-\(x^2-x\)=3x). The like \(x^2\) terms cancel out.
Step 3
Exam Tip
((f-g)(x)=x-2 +2x-\(x^2-x\)=3x)। समान \(x^2\) पद कट जाते हैं।
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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)
Explanation opens after your attempt
Step 1
Concept
((fg)(0)=f(0)g(0)=2\cdot1=2). First find the value of both functions.
Step 2
Why this answer is correct
The correct answer is A. (2). ((fg)(0)=f(0)g(0)=2\cdot1=2). First find the value of both functions.
Step 3
Exam Tip
((fg)(0)=f(0)g(0)=2\cdot1=2)। पहले दोनों फलनों का मान निकालें।
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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)
Explanation opens after your attempt
Step 1
Concept
((f-g)(2)=f(2)-g(2)=7-3=4). Sometimes simplifying first saves time.
Step 2
Why this answer is correct
The correct answer is A. (4). ((f-g)(2)=f(2)-g(2)=7-3=4). Sometimes simplifying first saves time.
Step 3
Exam Tip
((f-g)(2)=f(2)-g(2)=7-3=4)। कभी-कभी पहले सरल करने से समय बचता है।
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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)
Explanation opens after your attempt
Step 1
Concept
((f+g)(-1)=f(-1)+g(-1)=-1+(-5)=-6). Check signs carefully for negative input.
Step 2
Why this answer is correct
The correct answer is A. (-8). ((f+g)(-1)=f(-1)+g(-1)=-1+(-5)=-6). Check signs carefully for negative input.
Step 3
Exam Tip
((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।
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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. \(\frac{5}{2}\)
Step 1
Concept
(\left\(\frac{f}{g}\right\)(1)=\frac{f(1)}{g(1)}=\frac{5}{2}). The denominator value is (2), so division is allowed.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5}{2}\). (\left\(\frac{f}{g}\right\)(1)=\frac{f(1)}{g(1)}=\frac{5}{2}). The denominator value is (2), so division is allowed.
Step 3
Exam Tip
(\left\(\frac{f}{g}\right\)(1)=\frac{f(1)}{g(1)}=\frac{5}{2})। हर का मान (2) है, इसलिए भाग संभव है।
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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)
Explanation opens after your attempt
Step 1
Concept
((f+g)(4)=\sqrt{4}+5=2+5=7). For radical functions, substitute only defined values.
Step 2
Why this answer is correct
The correct answer is A. (7). ((f+g)(4)=\sqrt{4}+5=2+5=7). For radical functions, substitute only defined values.
Step 3
Exam Tip
((f+g)(4)=\sqrt{4}+5=2+5=7)। मूल वाले फलन में परिभाषित मान ही रखें।
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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)
Explanation opens after your attempt
Step 1
Concept
((fg)(9)=92 \cdot\sqrt{9}=81\cdot3=243). Finding separate values first is easier.
Step 2
Why this answer is correct
The correct answer is A. (243). ((fg)(9)=92 \cdot\sqrt{9}=81\cdot3=243). Finding separate values first is easier.
Step 3
Exam Tip
((fg)(9)=92 \cdot\sqrt{9}=81\cdot3=243)। गुणन से पहले अलग-अलग मान निकालना आसान है।
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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)
Explanation opens after your attempt
Step 1
Concept
((fg)(2)=\frac{1}{2}\cdot2=1). Remember the condition \(x\neq0\) for reciprocal functions.
Step 2
Why this answer is correct
The correct answer is A. (1). ((fg)(2)=\frac{1}{2}\cdot2=1). Remember the condition \(x\neq0\) for reciprocal functions.
Step 3
Exam Tip
((fg)(2)=\frac{1}{2}\cdot2=1)। भिन्न फलन में \(x\neq0\) शर्त याद रखें।
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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 \(\frac{1}{3}\)
Explanation opens after your attempt
Step 1
Concept
(\left\(\frac{f}{g}\right\)(0)=\frac{6}{2}=3). The denominator is not (0), so the value is valid.
Step 2
Why this answer is correct
The correct answer is A. (3). (\left\(\frac{f}{g}\right\)(0)=\frac{6}{2}=3). The denominator is not (0), so the value is valid.
Step 3
Exam Tip
(\left\(\frac{f}{g}\right\)(0)=\frac{6}{2}=3)। हर (0) नहीं है, इसलिए मान मान्य है।
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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
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A \(a^2-b^2\)
B \(a^2+2ab+b^2\)
C \(a^3+b^3\)
D \(a^2-2ab+b^2\)
Explanation opens after your attempt
Correct Answer
A. \(a^2-b^2\)
Step 1
Concept
The identity \(a^2-b^2\) applies to ((x-1)(x+1)). It gives ((fg)(x)=x-2 -1).
Step 2
Why this answer is correct
The correct answer is A. \(a^2-b^2\). The identity \(a^2-b^2\) applies to ((x-1)(x+1)). It gives ((fg)(x)=x-2 -1).
Step 3
Exam Tip
((x-1)(x+1)) में \(a^2-b^2\) पहचान लगती है। इससे ((fg)(x)=x-2 -1) मिलता है।
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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)
Explanation opens after your attempt
Step 1
Concept
((f+g)(3)=f(3)+g(3)=9+7=16). Substitute (x=3) in (2x+1) carefully.
Step 2
Why this answer is correct
The correct answer is A. (16). ((f+g)(3)=f(3)+g(3)=9+7=16). Substitute (x=3) in (2x+1) carefully.
Step 3
Exam Tip
((f+g)(3)=f(3)+g(3)=9+7=16)। मान रखते समय (2x+1) में (x=3) रखें।
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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
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A \(x^2-5\)
B \(3x^2+5\)
C \(x^2+5\)
D \(3x^2-5\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-5\)
Step 1
Concept
((f-g)(x)=2x-2 -\(x^2+5\)=x-2 -5). Change signs while removing the bracket.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-5\). ((f-g)(x)=2x-2 -\(x^2+5\)=x-2 -5). Change signs while removing the bracket.
Step 3
Exam Tip
((f-g)(x)=2x-2 -\(x^2+5\)=x-2 -5)। कोष्ठक हटाते समय चिह्न बदलें।
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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
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A \(x^2+3x\)
B (2x+3)
C \(x^2+3\)
D \(3x^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x\)
Step 1
Concept
((fg)(x)=(x+3)x=x-2 +3x). Use the distributive law for multiplication.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x\). ((fg)(x)=(x+3)x=x-2 +3x). Use the distributive law for multiplication.
Step 3
Exam Tip
((fg)(x)=(x+3)x=x-2 +3x)। वितरक नियम से गुणा करें।
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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
Step 1
Concept
((f+g)(x)=(2x-3)+(x+4)=3x+1). Add like terms separately.
Step 2
Why this answer is correct
The correct answer is A. (3x+1). ((f+g)(x)=(2x-3)+(x+4)=3x+1). Add like terms separately.
Step 3
Exam Tip
((f+g)(x)=(2x-3)+(x+4)=3x+1)। समान पदों को अलग-अलग जोड़ें।
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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
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A \(5-x^2\)
B \(x^2-5\)
C \(5x^2\)
D \(x^2+5\)
Explanation opens after your attempt
Correct Answer
A. \(5-x^2\)
Step 1
Concept
((f-g)(x)=5-x-2 ). If the order changes, the answer becomes \(x^2-5\), so order is important.
Step 2
Why this answer is correct
The correct answer is A. \(5-x^2\). ((f-g)(x)=5-x-2 ). If the order changes, the answer becomes \(x^2-5\), so order is important.
Step 3
Exam Tip
((f-g)(x)=5-x-2 )। क्रम बदलने से उत्तर \(x^2-5\) हो जाएगा, इसलिए क्रम महत्वपूर्ण है।
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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)
Explanation opens after your attempt
Step 1
Concept
(\frac{x-2 -9}{x+3}=\frac{(x-3)(x+3)}{x+3}=x-3), where \(x\neq-3\). Write the condition before cancellation.
Step 2
Why this answer is correct
The correct answer is A. (x-3). (\frac{x-2 -9}{x+3}=\frac{(x-3)(x+3)}{x+3}=x-3), where \(x\neq-3\). Write the condition before cancellation.
Step 3
Exam Tip
(\frac{x-2 -9}{x+3}=\frac{(x-3)(x+3)}{x+3}=x-3), जहाँ \(x\neq-3\)। काटने से पहले शर्त लिखें।
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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)
Explanation opens after your attempt
Step 1
Concept
Since (x-2 +2x+1=(x+1)2 ), the quotient is (x+1). Do not forget to exclude (x=-1).
Step 2
Why this answer is correct
The correct answer is A. (x+1). Since (x-2 +2x+1=(x+1)2 ), the quotient is (x+1). Do not forget to exclude (x=-1).
Step 3
Exam Tip
क्योंकि (x-2 +2x+1=(x+1)2 ), इसलिए भागफल (x+1) है। (x=-1) हटाना न भूलें।
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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
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A (7)
B (12)
C (0)
D (10)
Explanation opens after your attempt
Step 1
Concept
((f+g)(5)=f(5)+g(5)=7+0=7). Even if one function value is zero, addition remains normal.
Step 2
Why this answer is correct
The correct answer is A. (7). ((f+g)(5)=f(5)+g(5)=7+0=7). Even if one function value is zero, addition remains normal.
Step 3
Exam Tip
((f+g)(5)=f(5)+g(5)=7+0=7)। किसी एक फलन का मान शून्य हो तो भी जोड़ सामान्य रहता है।
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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)
Explanation opens after your attempt
Step 1
Concept
((fg)(2)=f(2)g(2)=8\cdot4=32). In product questions, find both values separately.
Step 2
Why this answer is correct
The correct answer is A. (32). ((fg)(2)=f(2)g(2)=8\cdot4=32). In product questions, find both values separately.
Step 3
Exam Tip
((fg)(2)=f(2)g(2)=8\cdot4=32)। गुणन में दोनों मानों को अलग-अलग निकालें।
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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 \(2x^2+2\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2\)
Step 1
Concept
((f+g)(x)=x-2 -1+x-2 +1=2x-2 ). The constant terms (-1) and (1) cancel out.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2\). ((f+g)(x)=x-2 -1+x-2 +1=2x-2 ). The constant terms (-1) and (1) cancel out.
Step 3
Exam Tip
((f+g)(x)=x-2 -1+x-2 +1=2x-2 )। स्थिर पद (-1) और (1) कट जाते हैं।
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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. \(2x^2+5\)
Step 1
Concept
((f-g)(x)=3x-2 +1-\(x^2-4\)=2x-2 +5). Apply the minus sign to both inner terms.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+5\). ((f-g)(x)=3x-2 +1-\(x^2-4\)=2x-2 +5). Apply the minus sign to both inner terms.
Step 3
Exam Tip
((f-g)(x)=3x-2 +1-\(x^2-4\)=2x-2 +5)। ऋण को अंदर के दोनों पदों पर लगाएँ।
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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 \(x^2+2\)
Explanation opens after your attempt
Step 1
Concept
((fg)(x)=(x+1)\cdot2=2x+2). Multiplying by a constant function multiplies every term.
Step 2
Why this answer is correct
The correct answer is A. (2x+2). ((fg)(x)=(x+1)\cdot2=2x+2). Multiplying by a constant function multiplies every term.
Step 3
Exam Tip
((fg)(x)=(x+1)\cdot2=2x+2)। स्थिर फलन से गुणा करने पर हर पद गुणित होता है।
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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)
Explanation opens after your attempt
Step 1
Concept
(\left\(\frac{f}{g}\right\)(x)=\frac{8x+4}{4}=2x+1). Divide every numerator term by (4).
Step 2
Why this answer is correct
The correct answer is A. (2x+1). (\left\(\frac{f}{g}\right\)(x)=\frac{8x+4}{4}=2x+1). Divide every numerator term by (4).
Step 3
Exam Tip
(\left\(\frac{f}{g}\right\)(x)=\frac{8x+4}{4}=2x+1)। अंश के हर पद को (4) से भाग दें।
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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
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A (0)
B (2x-14)
C (14)
D \(x^2-49\)
Explanation opens after your attempt
Step 1
Concept
((f+g)(x)=(x-7)+(7-x)=0). These functions are additive inverses of each other.
Step 2
Why this answer is correct
The correct answer is A. (0). ((f+g)(x)=(x-7)+(7-x)=0). These functions are additive inverses of each other.
Step 3
Exam Tip
((f+g)(x)=(x-7)+(7-x)=0)। ये फलन एक-दूसरे के योगात्मक प्रतिलोम हैं।
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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
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A (10)
B (4x)
C (4x+10)
D (0)
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Step 1
Concept
((f-g)(x)=2x+5-(2x-5)=10). The (x) terms cancel out.
Step 2
Why this answer is correct
The correct answer is A. (10). ((f-g)(x)=2x+5-(2x-5)=10). The (x) terms cancel out.
Step 3
Exam Tip
((f-g)(x)=2x+5-(2x-5)=10)। (x) पद कट जाते हैं।
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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
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A \(x^5\)
B \(x^6\)
C \(2x^3\)
D \(x^3+x^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^5\)
Step 1
Concept
((fg)(x)=x-2 \cdot x-3 =x-5 ). In multiplication with the same base, powers are added.
Step 2
Why this answer is correct
The correct answer is A. \(x^5\). ((fg)(x)=x-2 \cdot x-3 =x-5 ). In multiplication with the same base, powers are added.
Step 3
Exam Tip
((fg)(x)=x-2 \cdot x-3 =x-5 )। समान आधार के गुणन में घातें जुड़ती हैं।
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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
50 50-50 2 wrong hide
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A \(x^2\)
B \(x^6\)
C \(x^8\)
D (x)
Explanation opens after your attempt
Correct Answer
A. \(x^2\)
Step 1
Concept
(\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.
Step 2
Why this answer is correct
The correct answer is A. \(x^2\). (\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.
Step 3
Exam Tip
(\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।
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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
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#domain
#function addition
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A \(\mathbb{R}\)
B \(\mathbb{R}-{0}\)
C ({1,2})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}\)
Step 1
Concept
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.
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}\). 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.
Step 3
Exam Tip
दोनों रैखिक फलन पूरे \(\mathbb{R}\) पर परिभाषित हैं, इसलिए योग का डोमेन भी \(\mathbb{R}\) है। डोमेन में साझा मान देखें।
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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
50 50-50 2 wrong hide
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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. \(\mathbb{R}-{0}\)
Step 1
Concept
In \(\frac{1}{x}\), (x=0) is not allowed, so the domain of the sum is \(\mathbb{R}-{0}\). Take the common domain.
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}-{0}\). In \(\frac{1}{x}\), (x=0) is not allowed, so the domain of the sum is \(\mathbb{R}-{0}\). Take the common domain.
Step 3
Exam Tip
\(\frac{1}{x}\) में (x=0) मान्य नहीं है, इसलिए योग का डोमेन \(\mathbb{R}-{0}\) है। साझा डोमेन लें।
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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. \(\mathbb{R}-{3}\)
Step 1
Concept
In division, the denominator (g(x)=x-3) must not be zero, so \(x\neq3\). Hence the domain is \(\mathbb{R}-{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}-{3}\). In division, the denominator (g(x)=x-3) must not be zero, so \(x\neq3\). Hence the domain is \(\mathbb{R}-{3}\).
Step 3
Exam Tip
भाग में हर (g(x)=x-3) शून्य नहीं होना चाहिए, इसलिए \(x\neq3\)। अतः डोमेन \(\mathbb{R}-{3}\) है।
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