Class 12 composition of functions MCQ Questions

Question 1/12 Medium Mathematics Relations and Functions Onto function Class 12 Level 25

यदि \(f:A\to B\) आच्छादी है और \(g:B\to C\) आच्छादी है, तो \(g\circ f:A\to C\) के बारे में क्या कहा जा सकता है?

If \(f:A\to B\) is onto and \(g:B\to C\) is onto, what can be said about \(g\circ f:A\to C\)?

Explanation opens after your attempt

Correct Answer

A. यह आच्छादी होगाIt will be onto

Step 1

Concept

(C) का कोई भी अवयव (c) लें। / Take any element (c) of (C).

Step 2

Why this answer is correct

(g) आच्छादी है, इसलिए कोई \(b\in B\) है जिससे (g(b)=c); और (f) आच्छादी है, इसलिए कोई \(a\in A\) है जिससे (f(a)=b)। / Since (g) is onto, some \(b\in B\) has (g(b)=c); since (f) is onto, some \(a\in A\) has (f(a)=b).

Step 3

Exam Tip

इसलिए (\(g\circ f\)(a)=c), अतः संयोजन आच्छादी है। / Therefore (\(g\circ f\)(a)=c), so the composition is onto.

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Question 2/12 Expert Mathematics Relations and Functions One-one function Class 12 Level 24

यदि \(f:A\to B\) और \(g:B\to C\) हैं तथा \(g\circ f\) एकैकी है, तो कौन-सा निष्कर्ष हमेशा सही है?

If \(f:A\to B\) and \(g:B\to C\), and \(g\circ f\) is one-one, which conclusion is always correct?

Explanation opens after your attempt

Correct Answer

A. \(f\) एकैकी है(f) is one-one

Step 1

Concept

मान लें (f(a)=f(b))। / Suppose (f(a)=f(b)).

Step 2

Why this answer is correct

तब (g(f(a))=g(f(b))), यानी (\(g\circ f\)(a)=\(g\circ f\)(b))। चूंकि \(g\circ f\) एकैकी है, इसलिए (a=b)। / Then (g(f(a))=g(f(b))), meaning (\(g\circ f\)(a)=\(g\circ f\)(b)). Since \(g\circ f\) is one-one, (a=b).

Step 3

Exam Tip

संयोजन में बाएं वाले फलन के एकैकी होने का निष्कर्ष ऐसे निकाला जाता है। / In composition, this is how one concludes that the first function is one-one.

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Question 3/12 Expert Mathematics Relations and Functions One-one function Class 12 Level 23

यदि \(g\circ f\) एकैकी है, तो निश्चित रूप से कौन-सा निष्कर्ष सही है?

If \(g\circ f\) is one-one, which conclusion is definitely correct?

Explanation opens after your attempt

Correct Answer

A. \(f\) एकैकी है(f) is one-one

Step 1

Concept

मान लें (f(a)=f(b))। / Suppose (f(a)=f(b)).

Step 2

Why this answer is correct

तब (g(f(a))=g(f(b))), यानी (\(g\circ f\)(a)=\(g\circ f\)(b))। \(g\circ f\) एकैकी है, इसलिए (a=b)। / Then (g(f(a))=g(f(b))), so (\(g\circ f\)(a)=\(g\circ f\)(b)). Since \(g\circ f\) is one-one, (a=b).

Step 3

Exam Tip

संयोजन वाले प्रश्नों में परिभाषा को सीधे लागू करें। / In composition questions, apply the definition directly.

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Question 4/12 Hard Mathematics Relations and Functions One-one function Class 12 Level 24

यदि \(f:A\to B\) और \(g:B\to C\) दोनों एक-एक हैं, तो \(g\circ f\) के बारे में सही कथन क्या है?

If \(f:A\to B\) and \(g:B\to C\) are both one-one, what is the correct statement about \(g\circ f\)?

Explanation opens after your attempt

Correct Answer

A. \(g\circ f\) एक-एक है\(g\circ f\) is one-one

Step 1

Concept

मान लें (\(g\circ f\)\(x_1\)=\(g\circ f\)\(x_2\))। / Assume (\(g\circ f\)\(x_1\)=\(g\circ f\)\(x_2\)).

Step 2

Why this answer is correct

(g) एक-एक है, इसलिए (f\(x_1\)=f\(x_2\)), और (f) एक-एक है, इसलिए \(x_1=x_2\)। / Since (g) is one-one, (f\(x_1\)=f\(x_2\)), and since (f) is one-one, \(x_1=x_2\).

Step 3

Exam Tip

दो एक-एक फलनों का संयोजन भी एक-एक होता है। / The composition of two one-one functions is one-one.

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Question 5/12 Hard Mathematics Relations and Functions Functions Class 12 Level 19

यदि \(f:\mathbb{R}\to\mathbb{R}\) और \(g:\mathbb{R}\to\mathbb{R}\) इस प्रकार हैं कि (f(x)=x+3), (g(x)=x^-2), तो (\(g\circ f\)(x)) क्या है?

If \(f:\mathbb{R}\to\mathbb{R}\) and \(g:\mathbb{R}\to\mathbb{R}\) are given by (f(x)=x+3), (g(x)=x^-2), what is (\(g\circ f\)(x))?

Explanation opens after your attempt

Correct Answer

B. ((x+3)²)

Step 1

Concept

(\(g\circ f\)(x)) का अर्थ (g(f(x))) है। / (\(g\circ f\)(x)) means (g(f(x))).

Step 2

Why this answer is correct

(f(x)=x+3) को (g) में रखने पर (g(x+3)=(x+3)²) मिलता है। / Substituting (f(x)=x+3) into (g) gives (g(x+3)=(x+3)²).

Step 3

Exam Tip

संयोजन में क्रम बदलने से उत्तर बदल सकता है। / In composition, changing the order can change the answer.

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Question 6/12 Medium Mathematics Relations and Functions Functions Class 12 Level 21

यदि (f(x)=2x+1) और (g(x)=x^-2+3), तो (\(g\circ f\)(1)) का मान क्या होगा?

If (f(x)=2x+1) and (g(x)=x^-2+3), what is the value of (\(g\circ f\)(1))?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

(\(g\circ f\)(1)=g(f(1))) होता है। / (\(g\circ f\)(1)=g(f(1))).

Step 2

Why this answer is correct

(f(1)=2\cdot1+1=3)। / (f(1)=2\cdot1+1=3).

Step 3

Exam Tip

(g(3)=3²+3=12), इसलिए मान (12) है। / (g(3)=3²+3=12), so the value is (12).

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Question 7/12 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि (f(x)=x-2) और (g(x)=x^-2+1), तो (\(g\circ f\)(4)) का मान क्या होगा?

If (f(x)=x-2) and (g(x)=x^-2+1), what is the value of (\(g\circ f\)(4))?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

(\(g\circ f\)(4)=g(f(4))) होता है। / (\(g\circ f\)(4)=g(f(4))).

Step 2

Why this answer is correct

(f(4)=4-2=2)। / (f(4)=4-2=2).

Step 3

Exam Tip

(g(2)=2²+1=5)। / (g(2)=2²+1=5).

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Question 8/12 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f(x)=2x+1) और (g(x)=x^-2-1), तो (\(g\circ f\)(2)) का मान क्या होगा?

If (f(x)=2x+1) and (g(x)=x^-2-1), what is the value of (\(g\circ f\)(2))?

Explanation opens after your attempt

Correct Answer

A. (24)

Step 1

Concept

(\(g\circ f\)(2)=g(f(2)))। / (\(g\circ f\)(2)=g(f(2))).

Step 2

Why this answer is correct

(f(2)=2\cdot2+1=5)। / (f(2)=2\cdot2+1=5).

Step 3

Exam Tip

(g(5)=5²-1=24), इसलिए उत्तर (24) है। / (g(5)=5²-1=24), so the answer is (24).

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Question 9/12 Easy Mathematics Relations and Functions Functions Class 12 Level 21

यदि (f(x)=x+2) और (g(x)=3x), तो (\(f\circ g\)(2)) क्या होगा?

If (f(x)=x+2) and (g(x)=3x), what is (\(f\circ g\)(2))?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

(\(f\circ g\)(2)=f(g(2)))। / (\(f\circ g\)(2)=f(g(2))).

Step 2

Why this answer is correct

(g(2)=3\cdot2=6)। / (g(2)=3\cdot2=6).

Step 3

Exam Tip

(f(6)=6+2=8)। / (f(6)=6+2=8).

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Question 10/12 Easy Mathematics Relations and Functions Functions Class 12 Level 20

यदि (f(x)=x^-2) और (g(x)=x+1), तो (\(f\circ g\)(2)) क्या होगा?

If (f(x)=x^-2) and (g(x)=x+1), what is (\(f\circ g\)(2))?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

(\(f\circ g\)(2)=f(g(2)))। / (\(f\circ g\)(2)=f(g(2))).

Step 2

Why this answer is correct

(g(2)=3)। / (g(2)=3).

Step 3

Exam Tip

(f(3)=3²=9), इसलिए मान (9) है। / (f(3)=3²=9), so the value is (9).

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Question 11/12 Easy Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f(x)=2x+1) और (g(x)=x^-2), तो (\(g\circ f\)(1)) क्या होगा?

If (f(x)=2x+1) and (g(x)=x^-2), what is (\(g\circ f\)(1))?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

(\(g\circ f\)(1)=g(f(1)))। / (\(g\circ f\)(1)=g(f(1))).

Step 2

Why this answer is correct

(f(1)=2\cdot1+1=3)। / (f(1)=2\cdot1+1=3).

Step 3

Exam Tip

(g(3)=3²=9), इसलिए मान (9) है। / (g(3)=3²=9), so the value is (9).

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Question 12/12 Easy Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f(x)=x+1) और (g(x)=2x), तो (\(f\circ g\)(3)) का मान क्या है?

If (f(x)=x+1) and (g(x)=2x), what is the value of (\(f\circ g\)(3))?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

(\(f\circ g\)(3)=f(g(3))) होता है। / (\(f\circ g\)(3)=f(g(3))).

Step 2

Why this answer is correct

(g(3)=2\cdot3=6)। / (g(3)=2\cdot3=6).

Step 3

Exam Tip

(f(6)=6+1=7), इसलिए मान (7) है। / (f(6)=6+1=7), so the value is (7).

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composition of functions MCQ Questions for Class 12

Practice Questions

यदि \(f:A\to B\) आच्छादी है और \(g:B\to C\) आच्छादी है, तो \(g\circ f:A\to C\) के बारे में क्या कहा जा सकता है?

Concept

Why this answer is correct

Exam Tip

यदि \(f:A\to B\) और \(g:B\to C\) हैं तथा \(g\circ f\) एकैकी है, तो कौन-सा निष्कर्ष हमेशा सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(g\circ f\) एकैकी है, तो निश्चित रूप से कौन-सा निष्कर्ष सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(f:A\to B\) और \(g:B\to C\) दोनों एक-एक हैं, तो \(g\circ f\) के बारे में सही कथन क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(f:\mathbb{R}\to\mathbb{R}\) और \(g:\mathbb{R}\to\mathbb{R}\) इस प्रकार हैं कि (f(x)=x+3), (g(x)=x-2), तो (\(g\circ f\)(x)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=2x+1) और (g(x)=x-2+3), तो (\(g\circ f\)(1)) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2) और (g(x)=x-2+1), तो (\(g\circ f\)(4)) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=2x+1) और (g(x)=x-2-1), तो (\(g\circ f\)(2)) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x+2) और (g(x)=3x), तो (\(f\circ g\)(2)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2) और (g(x)=x+1), तो (\(f\circ g\)(2)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=2x+1) और (g(x)=x-2), तो (\(g\circ f\)(1)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x+1) और (g(x)=2x), तो (\(f\circ g\)(3)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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यदि \(f:\mathbb{R}\to\mathbb{R}\) और \(g:\mathbb{R}\to\mathbb{R}\) इस प्रकार हैं कि (f(x)=x+3), (g(x)=x^-2), तो (\(g\circ f\)(x)) क्या है?

यदि (f(x)=2x+1) और (g(x)=x^-2+3), तो (\(g\circ f\)(1)) का मान क्या होगा?

यदि (f(x)=x-2) और (g(x)=x^-2+1), तो (\(g\circ f\)(4)) का मान क्या होगा?

यदि (f(x)=2x+1) और (g(x)=x^-2-1), तो (\(g\circ f\)(2)) का मान क्या होगा?

यदि (f(x)=x^-2) और (g(x)=x+1), तो (\(f\circ g\)(2)) क्या होगा?

यदि (f(x)=2x+1) और (g(x)=x^-2), तो (\(g\circ f\)(1)) क्या होगा?