Let $\text{⨍ (x)=-1+}\left|\mathrm{x}-2\right|\text{,}$and $\mathrm{g}\left(\mathrm{x}\right)=1-\left|\mathrm{x}\right|$ then the set of all points where fog is discontinuous is

$\begin{array}{l}fog=f\left(g\right(x\left)\right)=f(1-|x\left|\right)\\ =-1+|1-|x|-2|\\ =-1+|-|x|-1|=-1+\left|1+\left|x\right|\right|\\ \\ \therefore fog\left(x\right)=-1+\left|1+\left|x\right|\right|\\ \Rightarrow fog\left(x\right)==\left\{\begin{array}{cc}-1+x+1,x\ge 0& \\ -1-x+1,& x<0\end{array}\right.\\ \Rightarrow fog\left(x\right)=\left\{\begin{array}{cc}x,& x\ge 0\\ -x,& x<0\end{array}\right.\\ fog\left(x\right) is continuous every where\end{array}$