Question

If $f\left(x\right)=|1-x|$, then the points where $si{n}^{-1}\left(f|x|\right)$ is non-differentiable are

• A. $\{0,1\}$
• B. $\{0,-1\}$
• C. $\{0,1,-1\}$
• D. None of these

Answer 1

The correct option is C $\{0,1,-1\}$

Given that $f\left(x\right)=|1-x|$
$\Rightarrow f\left(|x|\right)=\{\begin{array}{cc}x-1& x>1\\ 1-x& 0<x\le 1\\ 1+x& -1\le x\le 0\\ -x-1& x<-1\end{array}$
Clearly the domain of $si{n}^{-1}\left(f|x|\right)is[-1,1]$.
$\Rightarrow$ It is non differentiable at the points $\{-1,0,1\}$