If   $f\left(x\right)=\{\begin{array}{l}\sin x,x<0\\ \cos x-|x-1|, x\ge 0\end{array}$, then  $g\left(x\right)=f\left(\left|x\right|\right)$  is non –differentible for 

 $f\left(\left|x\right|\right)=\{\begin{array}{l}\sin \left|x\right|,\left|x\right|<0\\ \cos \left(x\right)-|\left|x\right|-1|,\left|x\right|\ge 0\end{array}$
=  $\cos \left(x\right)-|\left|x\right|-1|,x\in R$
Which is non-differentiable at x=0 and when 
$\left|x\right|-1=0orx=\pm 1$ .