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JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f: R \rightarrow R\) be defined as \(f( x )=2 x -1\) and \(g: R-\{1\} \rightarrow R\) be defined as \(g(x)=\frac{x-\frac{1}{2}}{x-1}\) Then the composition function \(f(g(x))\) is
- A onto but not one-one
- B both one-one and onto
- C one-one but not onto
- D neither one-one nor onto
Answer & Solution
Correct Answer
(C) one-one but not onto
Step-by-step Solution
Detailed explanation
\(f(g(x))=2 g(x)-1=2\left(\frac{2 x-1}{2(x-1)}\right)-1\) \(=\frac{x}{x-1}=1+\frac{1}{x-1}\) Range of \(f(g(x)= R -\{1\}\) Range of \(f(g(x))\) is not onto \(\&\) \(f(g(x))\) is one-one So \(f(g(x))\) is one-one but not onto.
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