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composition order MCQ Questions for Class 12

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3 questions tagged with composition order.

Question 1/3 Medium Mathematics Relations and Functions Functions Class 12 Level 21

यदि (f(x)=x-2-1) और (g(x)=x+2), तो (\(f\circ g\)(x)) और (\(g\circ f\)(x)) के बारे में सही कथन कौन-सा है?

If (f(x)=x-2-1) and (g(x)=x+2), which statement about (\(f\circ g\)(x)) and (\(g\circ f\)(x)) is correct?

Explanation opens after your attempt
Correct Answer

A. दोनों सामान्यतः समान नहीं हैंThey are generally not equal

Step 1

Concept

(\(f\circ g\)(x)=f(x+2)=(x+2)2-1).

Step 2

Why this answer is correct

(\(g\circ f\)(x)=g\(x^2-1\)=x-2+1).

Step 3

Exam Tip

The expressions are generally different, so order matters in composition. चरण 1: (\(f\circ g\)(x)=f(x+2)=(x+2)2-1)। चरण 2: (\(g\circ f\)(x)=g\(x^2-1\)=x-2+1)। चरण 3: दोनों व्यंजक सामान्यतः अलग हैं, इसलिए संयुक्त फलन में क्रम का ध्यान रखें।

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Question 2/3 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि (f(x)=x-2+2) और (g(x)=x-1), तो (\(f\circ g\)(x)) तथा (\(g\circ f\)(x)) के बारे में सही कथन कौन-सा है?

If (f(x)=x-2+2) and (g(x)=x-1), which statement about (\(f\circ g\)(x)) and (\(g\circ f\)(x)) is correct?

Explanation opens after your attempt
Correct Answer

A. दोनों सामान्यतः समान नहीं हैंThey are generally not equal

Step 1

Concept

(\(f\circ g\)(x)=f(x-1)=(x-1)2+2).

Step 2

Why this answer is correct

(\(g\circ f\)(x)=g\(x^2+2\)=x-2+1).

Step 3

Exam Tip

The expressions are generally different, so order is important in composition. चरण 1: (\(f\circ g\)(x)=f(x-1)=(x-1)2+2)। चरण 2: (\(g\circ f\)(x)=g\(x^2+2\)=x-2+1)। चरण 3: दोनों व्यंजक सामान्यतः अलग हैं, इसलिए संयुक्त फलन में क्रम महत्वपूर्ण है।

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Question 3/3 Medium Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f(x)=x-2) और (g(x)=x+1), तो (\(f\circ g\)(x)) और (\(g\circ f\)(x)) के बारे में सही कथन कौन-सा है?

If (f(x)=x-2) and (g(x)=x+1), which statement about (\(f\circ g\)(x)) and (\(g\circ f\)(x)) is correct?

Explanation opens after your attempt
Correct Answer

A. दोनों हमेशा समान नहीं हैंThey are not always equal

Step 1

Concept

(\(f\circ g\)(x)=f(x+1)=(x+1)2).

Step 2

Why this answer is correct

(\(g\circ f\)(x)=g\(x^2\)=x-2+1).

Step 3

Exam Tip

These expressions are generally not equal, so order matters. चरण 1: (\(f\circ g\)(x)=f(x+1)=(x+1)2)। चरण 2: (\(g\circ f\)(x)=g\(x^2\)=x-2+1)। चरण 3: दोनों व्यंजक सामान्यतः समान नहीं हैं, इसलिए क्रम का ध्यान रखें।

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