यदि \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=x+4) और \(g:\mathbb{R}\to\mathbb{R}\), (g(x)=3x-2), तो \(g\circ f\) कैसा है?
If \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=x+4) and \(g:\mathbb{R}\to\mathbb{R}\), (g(x)=3x-2), what type is \(g\circ f\)?
#one-one function
#composition
#linear functions
A एकैकी / One-one
B एकैकी नहीं / Not one-one
C स्थिर / Constant
D परिभाषित नहीं / Not defined
Explanation opens after your attempt
Correct Answer
A. एकैकी / One-one
Step 1
Concept
(\(g\circ f\)(x)=g(x+4)=3(x+4)-2).
Step 2
Why this answer is correct
This is (3x+10), a linear function with coefficient \(3\ne 0\).
Step 3
Exam Tip
Such a linear composition is one-one. चरण 1: (\(g\circ f\)(x)=g(x+4)=3(x+4)-2)। चरण 2: यह (3x+10) है, जो रैखिक फलन है और (x) का गुणांक \(3\ne 0\) है। चरण 3: ऐसे रैखिक संयोजन को एकैकी माना जाएगा।
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यदि (f(x)=x+2) और (g(x)=3x-1), तो (\(f\circ g\)(x)- \(g\circ f\)(x)) का मान क्या है?
If (f(x)=x+2) and (g(x)=3x-1), what is the value of (\(f\circ g\)(x)-\(g\circ f\)(x))?
#functions
#composition
#linear functions
#exam
A (0)
B (2)
C (-4)
D (4)
Explanation opens after your attempt
Step 1
Concept
(f(g(x))=f(3x-1)=3x+1).
Step 2
Why this answer is correct
(g(f(x))=g(x+2)=3x+5).
Step 3
Exam Tip
The difference is (3x+1-(3x+5)=-4), so order matters in composition. चरण 1: (f(g(x))=f(3x-1)=3x+1)। चरण 2: (g(f(x))=g(x+2)=3x+5)। चरण 3: अंतर (3x+1-(3x+5)=-4) है, इसलिए क्रम बदलने से मान बदल सकता है।
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यदि \(f:\mathbb{R}\to\mathbb{R}\) और \(g:\mathbb{R}\to\mathbb{R}\) में (f(x)=x+1), (g(x)=2x), तो (\(f\circ g\)(x)) और (\(g\circ f\)(x)) के बारे में सही कथन कौन सा है?
If \(f:\mathbb{R}\to\mathbb{R}\) and \(g:\mathbb{R}\to\mathbb{R}\) are given by (f(x)=x+1), (g(x)=2x), which statement about (\(f\circ g\)(x)) and (\(g\circ f\)(x)) is correct?
#composition
#order of functions
#linear functions
A दोनों बराबर हैं / They are equal
B (\(f\circ g\)(x)=2x+1) और (\(g\circ f\)(x)=2x+2) / (\(f\circ g\)(x)=2x+1) and (\(g\circ f\)(x)=2x+2)
C (\(f\circ g\)(x)=x+2) और (\(g\circ f\)(x)=2x+1) / (\(f\circ g\)(x)=x+2) and (\(g\circ f\)(x)=2x+1)
D दोनों स्थिर हैं / Both are constant
Explanation opens after your attempt
Correct Answer
B. (\(f\circ g\)(x)=2x+1) और (\(g\circ f\)(x)=2x+2) / (\(f\circ g\)(x)=2x+1) and (\(g\circ f\)(x)=2x+2)
Step 1
Concept
(f(g(x))=f(2x)=2x+1).
Step 2
Why this answer is correct
(g(f(x))=g(x+1)=2x+2).
Step 3
Exam Tip
Composition of functions is not generally commutative. चरण 1: (f(g(x))=f(2x)=2x+1)। चरण 2: (g(f(x))=g(x+1)=2x+2)। चरण 3: फलनों का संयोजन सामान्यतः क्रमविनिमेय नहीं होता।
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यदि \(f:\mathbb{R}\to\mathbb{R}\) और \(g:\mathbb{R}\to\mathbb{R}\) में (f(x)=3x+1), (g(x)=x-4), तो (\(f\circ g\)(2)) का मान क्या है?
If \(f:\mathbb{R}\to\mathbb{R}\) and \(g:\mathbb{R}\to\mathbb{R}\) are given by (f(x)=3x+1), (g(x)=x-4), what is the value of (\(f\circ g\)(2))?
#composition
#value of function
#linear functions
A (-5)
B (-3)
C (3)
D (7)
Explanation opens after your attempt
Step 1
Concept
First find (g(2)=2-4=-2).
Step 2
Why this answer is correct
Then (f(-2)=3(-2)+1=-5).
Step 3
Exam Tip
In composition, apply the inner function first. चरण 1: पहले (g(2)=2-4=-2) निकालें। चरण 2: अब (f(-2)=3(-2)+1=-5) होगा। चरण 3: संयोजन के मान में अंदर वाले फलन को पहले लगाएँ।
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यदि (f(x)=5x+1) और (g(x)=x-4), तो (\(f\circ g\)(x)) क्या होगा?
If (f(x)=5x+1) and (g(x)=x-4), what is (\(f\circ g\)(x))?
#composition
#linear functions
#algebra
#medium
A (5x-19)
B (5x-3)
C (x+1)
D (5x+5)
Explanation opens after your attempt
Correct Answer
A. (5x-19)
Step 1
Concept
(\(f\circ g\)(x)=f(g(x))).
Step 2
Why this answer is correct
Put (g(x)=x-4) into (f).
Step 3
Exam Tip
(f(x-4)=5(x-4)+1=5x-19). चरण 1: (\(f\circ g\)(x)=f(g(x))) है। चरण 2: (g(x)=x-4) को (f) में रखें। चरण 3: (f(x-4)=5(x-4)+1=5x-19)।
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यदि (f(x)=3x-2) और (g(x)=x+5), तो (\(f\circ g\)(x)) क्या होगा?
If (f(x)=3x-2) and (g(x)=x+5), what is (\(f\circ g\)(x))?
#composition
#linear functions
#algebra
#medium
A (3x+13)
B (3x+3)
C (x+13)
D (3x-7)
Explanation opens after your attempt
Correct Answer
A. (3x+13)
Step 1
Concept
(\(f\circ g\)(x)=f(g(x))).
Step 2
Why this answer is correct
Put (g(x)=x+5) into (f).
Step 3
Exam Tip
(f(x+5)=3(x+5)-2=3x+13). चरण 1: (\(f\circ g\)(x)=f(g(x))) होता है। चरण 2: (g(x)=x+5) को (f) में रखें। चरण 3: (f(x+5)=3(x+5)-2=3x+13)।
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यदि (f(x)=x+3) और (g(x)=2x-1), तो (\(f\circ g\)(x)) क्या होगा?
If (f(x)=x+3) and (g(x)=2x-1), what is (\(f\circ g\)(x))?
#composition
#linear functions
#algebra
#medium
A (2x+2)
B (2x-4)
C (2x+3)
D (x+2)
Explanation opens after your attempt
Step 1
Concept
(\(f\circ g\)(x)=f(g(x))).
Step 2
Why this answer is correct
Put (g(x)=2x-1) into (f).
Step 3
Exam Tip
(f(2x-1)=2x-1+3=2x+2). चरण 1: (\(f\circ g\)(x)=f(g(x))) होता है। चरण 2: (g(x)=2x-1) को (f) में रखें। चरण 3: (f(2x-1)=2x-1+3=2x+2)।
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यदि (f(x)=3x) और (g(x)=\frac{x}{3}), तो (f) और (g) के बारे में सही कथन कौन-सा है?
If (f(x)=3x) and (g(x)=\frac{x}{3}), which statement about (f) and (g) is correct?
#inverse functions
#composition
#linear functions
A वे एक-दूसरे के प्रतिलोम हैं / They are inverses of each other
B वे दोनों स्थिर फलन हैं / Both are constant functions
C वे समान फलन हैं / They are the same function
D वे फलन नहीं हैं / They are not functions
Explanation opens after your attempt
Correct Answer
A. वे एक-दूसरे के प्रतिलोम हैं / They are inverses of each other
Step 1
Concept
(f(g(x))=f\(\frac{x}{3}\)=x).
Step 2
Why this answer is correct
(g(f(x))=g(3x)=x).
Step 3
Exam Tip
Both composites give the identity function, so they are inverses. चरण 1: (f(g(x))=f\(\frac{x}{3}\)=x)। चरण 2: (g(f(x))=g(3x)=x)। चरण 3: दोनों संयुक्त फलन पहचान फलन देते हैं, इसलिए दोनों प्रतिलोम हैं।
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यदि (f(x)=2x-1) और (g(x)=x+4), तो (\(g\circ f\)(2)) क्या होगा?
If (f(x)=2x-1) and (g(x)=x+4), what is (\(g\circ f\)(2))?
#composition
#function evaluation
#linear functions
A (7)
B (6)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(\(g\circ f\)(2)=g(f(2))).
Step 2
Why this answer is correct
(f(2)=2\cdot2-1=3).
Step 3
Exam Tip
(g(3)=3+4=7). चरण 1: (\(g\circ f\)(2)=g(f(2)))। चरण 2: (f(2)=2\cdot2-1=3)। चरण 3: (g(3)=3+4=7)।
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यदि (f(x)=2x) और (g(x)=\frac{x}{2}), तो (f) और (g) के बारे में सही कथन कौन-सा है?
If (f(x)=2x) and (g(x)=\frac{x}{2}), which statement about (f) and (g) is correct?
#inverse functions
#composition
#linear functions
#class 12
A वे एक-दूसरे के प्रतिलोम हैं / They are inverses of each other
B वे दोनों स्थिर फलन हैं / Both are constant functions
C वे समान फलन हैं / They are the same function
D वे फलन नहीं हैं / They are not functions
Explanation opens after your attempt
Correct Answer
A. वे एक-दूसरे के प्रतिलोम हैं / They are inverses of each other
Step 1
Concept
(f(g(x))=f\(\frac{x}{2}\)=x).
Step 2
Why this answer is correct
(g(f(x))=g(2x)=x).
Step 3
Exam Tip
Both composites give the identity function, so they are inverses. चरण 1: (f(g(x))=f\(\frac{x}{2}\)=x)। चरण 2: (g(f(x))=g(2x)=x)। चरण 3: दोनों संयुक्त फलन पहचान फलन देते हैं, इसलिए वे प्रतिलोम हैं।
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यदि (f(x)=2x+3) और (g(x)=x-1), तो (\(f\circ g\)(x)) क्या होगा?
If (f(x)=2x+3) and (g(x)=x-1), what is (\(f\circ g\)(x))?
#composition
#linear functions
#algebra
#easy
A (2x+1)
B (2x+2)
C (2x-1)
D (x+2)
Explanation opens after your attempt
Step 1
Concept
(\(f\circ g\)(x)=f(g(x))).
Step 2
Why this answer is correct
Put (g(x)=x-1) into (f).
Step 3
Exam Tip
(f(x-1)=2(x-1)+3=2x+1). चरण 1: (\(f\circ g\)(x)=f(g(x)))। चरण 2: (g(x)=x-1) को (f) में रखें। चरण 3: (f(x-1)=2(x-1)+3=2x+1)।
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यदि (f(x)=x+4) और (g(x)=2x), तो (\(g\circ f\)(1)) क्या होगा?
If (f(x)=x+4) and (g(x)=2x), what is (\(g\circ f\)(1))?
#composition
#function value
#linear functions
#class 12
A (10)
B (6)
C (9)
D (8)
Explanation opens after your attempt
Step 1
Concept
(\(g\circ f\)(1)=g(f(1))).
Step 2
Why this answer is correct
(f(1)=1+4=5).
Step 3
Exam Tip
(g(5)=2\cdot5=10). चरण 1: (\(g\circ f\)(1)=g(f(1)))। चरण 2: (f(1)=1+4=5)। चरण 3: (g(5)=2\cdot5=10)।
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यदि (f(x)=3x) और (g(x)=x+1), तो ((f-g)(x)) क्या होगा?
If (f(x)=3x) and (g(x)=x+1), what is ((f-g)(x))?
#difference of functions
#function operations
#linear functions
A (2x-1)
B (4x+1)
C (2x+1)
D \(3x^2+x\)
Explanation opens after your attempt
Step 1
Concept
((f-g)(x)=f(x)-g(x)).
Step 2
Why this answer is correct
(3x-(x+1)=3x-x-1).
Step 3
Exam Tip
Simplifying gives (2x-1). चरण 1: ((f-g)(x)=f(x)-g(x))। चरण 2: (3x-(x+1)=3x-x-1)। चरण 3: सरल करने पर (2x-1) मिलता है।
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यदि (f(x)=2x) और (g(x)=x-1), तो ((f+g)(x)) क्या होगा?
If (f(x)=2x) and (g(x)=x-1), what is ((f+g)(x))?
#sum of functions
#function operations
#linear functions
A (3x-1)
B (x-1)
C \(2x^2-1\)
D (3x+1)
Explanation opens after your attempt
Step 1
Concept
((f+g)(x)=f(x)+g(x)).
Step 2
Why this answer is correct
(2x+(x-1)=3x-1).
Step 3
Exam Tip
In the sum of functions, add their values. चरण 1: ((f+g)(x)=f(x)+g(x)) होता है। चरण 2: (2x+(x-1)=3x-1)। चरण 3: फलनों के योग में उनके मानों को जोड़ा जाता है।
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