Let $f, g: \mathbf{R} \rightarrow \mathbf{R}$ be defined as : $f(x)=|x-1| \text { and } g(x)= \begin{cases}\mathrm{e}^x, \text { MARA } & x \geq 0 \\ x+1, & x \leq 0\end{cases}$
Then the function $f(g(x))$ is

• Correct answer
  A

  neither one-one nor onto.
• B

  one-one but not onto.
• C

  onto but not one-one.
• D

  both one-one and onto.

Solution

$\begin{aligned} & f(g(x))=|g(x)-1| \\ & f o g\left[\begin{array}{cc}\left|e^x-1\right| & x \geq 0 \\ |x+1-1| & x \leq 0\end{array}\right. \\ & \text { fog }\left[\begin{array}{cc}e^x-1 & x \geq 0 \\ -x & x \leq 0\end{array}\right.\end{aligned}$

Hence, the correct answer is option: 'A'.