JEE Mains · Maths · STD 12 - 1. relation and function
Let \( f, \mathrm{~g}: \mathrm{R} \rightarrow \mathrm{R}\) be defined as : \(f(\mathrm{x})=|\mathrm{x}-1|\) and \(g(x)=\left\{\begin{array}{cc}\mathrm{e}^{\mathrm{x}}, & \mathrm{x} \geq 0 \\ \mathrm{x}+1, & \mathrm{x} \leq 0\end{array}\right.\). Then the function \(f(\mathrm{~g}(\mathrm{x}))\) is
- A neither one-one nor onto.
- B one-one but not onto.
- C both one-one and onto.
- D onto but not one-one.
Answer & Solution
Correct Answer
(A) neither one-one nor onto.
Step-by-step Solution
Detailed explanation
\(f(g(x))=|g(x)-1|\) fog \(\left[\begin{array}{cc}\left|e^x-1\right| & x \geq 0 \\ |x+1-1| & x \leq 0\end{array}\right.\) \(f o g\left[\begin{array}{cc}e^x-1 & x \geq 0 \\ -x & x \leq 0\end{array}\right.\)
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