Given,
f(x)={\begin{matrix}x+1,x<0 \\ |x-1|,x\geq 0\end{matrix}and g(x)={\begin{matrix}x+1,x<0 \\ 1,x\geq 0\end{matrix}
\Rightarrow f(x)={\begin{matrix}x+1, & x<0 \\ 1-x, & 0\leq x<1 \\ x-1, & x>1\end{matrix}&g(x)={\begin{matrix}1+x, & x<0 \\ 1, & x\geq 0\end{matrix}
Now, for gof(x)
gof(x)={\begin{matrix}1+f(x), & f(x)<0,x<0 \\ 1, & f(x)\geq 0,x\geq 0\end{matrix}
\Rightarrow gof(x)={\begin{matrix}x+2, & x<-1 \\ 1, & x\geq -1\end{matrix}
Now plotting the diagram we get,
Now from above diagram we can say that function is continuous but not differentiable at x=−1 due to sharp corner.