If $f (x) =\left\{\begin{matrix} |x|,& x ≤1\\2-x,&x>1\end{matrix}\right.$ then $fof (x)$ is equal to

$\left\{\begin{matrix}2-|x|,&x<-1\\|x|,& -1≤x ≤1\\|2-x|,&x>1\end{matrix}\right.$

We have,

$fof (x) = f (f(x))$

$⇒fof (x)=\left\{\begin{matrix}f(|x|),&x ≤1\\f(2-x),&x>1\end{matrix}\right.$

$⇒fof (x)=\left\{\begin{matrix}||x||,&if\,-1≤x ≤1\\2-|x|,&if\, x <-1\\|2-x|,&x>1\end{matrix}\right.$

$⇒fof (x)=\left\{\begin{matrix}||x||,&if\,-1≤x ≤1\\2-|x|,&if\, x <-1\\|2-x|,&if\,x>1\end{matrix}\right.$