यदि \(f:\mathbb{R}\to\mathbb{R}\) और \(g:\mathbb{R}\to\mathbb{R}\) दोनों एकैकी हैं, तो \(g\circ f\) के बारे में सही कथन कौन सा है?
If \(f:\mathbb{R}\to\mathbb{R}\) and \(g:\mathbb{R}\to\mathbb{R}\) are both one-one, which statement about \(g\circ f\) is correct?
Explanation opens after your attempt
Correct Answer
A. यह हमेशा एकैकी हैIt is always one-one
Concept
Suppose (\(g\circ f\)\(x_1\)=\(g\circ f\)\(x_2\)).
Why this answer is correct
Since (g) is one-one, (f\(x_1\)=f\(x_2\)); since (f) is one-one, \(x_1=x_2\).
Exam Tip
The composition of one-one functions is one-one. चरण 1: मान लें (\(g\circ f\)\(x_1\)=\(g\circ f\)\(x_2\))। चरण 2: (g) एकैकी है, इसलिए (f\(x_1\)=f\(x_2\)); फिर (f) एकैकी है, इसलिए \(x_1=x_2\)। चरण 3: एकैकी फलनों का संयोजन फिर एकैकी होता है।
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