Class 12 Mathematics Relations and Functions One-one function Expert Level 22

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

If \(f\circ g\) is one-one, which statement is definitely true?

Explanation opens after your attempt
Correct Answer

C. (g) एक-एक है(g) is one-one

Step 1

Concept

Suppose (g\(x_1\)=g\(x_2\)).

Step 2

Why this answer is correct

Then (f(g\(x_1\))=f(g\(x_2\))), so (\(f\circ g\)\(x_1\)=\(f\circ g\)\(x_2\)).

Step 3

Exam Tip

Since \(f\circ g\) is one-one, \(x_1=x_2\), hence (g) is one-one. चरण 1: मान लें (g\(x_1\)=g\(x_2\))। चरण 2: तब (f(g\(x_1\))=f(g\(x_2\))), अर्थात (\(f\circ g\)\(x_1\)=\(f\circ g\)\(x_2\))। चरण 3: \(f\circ g\) एक-एक है, इसलिए \(x_1=x_2\), अतः (g) एक-एक है।

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Mathematics Answer, Explanation and Revision Hints

यदि \(f\circ g\) एक-एक है, तो कौन सा कथन निश्चित रूप से सही है? / If \(f\circ g\) is one-one, which statement is definitely true?

Correct Answer: C. (g) एक-एक है / (g) is one-one. Explanation: चरण 1: मान लें (g\(x_1\)=g\(x_2\))। चरण 2: तब (f(g\(x_1\))=f(g\(x_2\))), अर्थात (\(f\circ g\)\(x_1\)=\(f\circ g\)\(x_2\))। चरण 3: \(f\circ g\) एक-एक है, इसलिए \(x_1=x_2\), अतः (g) एक-एक है। / Step 1: Suppose (g\(x_1\)=g\(x_2\)). Step 2: Then (f(g\(x_1\))=f(g\(x_2\))), so (\(f\circ g\)\(x_1\)=\(f\circ g\)\(x_2\)). Step 3: Since \(f\circ g\) is one-one, \(x_1=x_2\), hence (g) is one-one.

Which concept should I revise for this Mathematics MCQ?

Suppose (g\(x_1\)=g\(x_2\)).

What exam hint can help solve this Mathematics question?

Since \(f\circ g\) is one-one, \(x_1=x_2\), hence (g) is one-one. चरण 1: मान लें (g\(x_1\)=g\(x_2\))। चरण 2: तब (f(g\(x_1\))=f(g\(x_2\))), अर्थात (\(f\circ g\)\(x_1\)=\(f\circ g\)\(x_2\))। चरण 3: \(f\circ g\) एक-एक है, इसलिए \(x_1=x_2\), अतः (g) एक-एक है।