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

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