Limits Continuity And Differentiability

Define $f(x)=\left\{\begin{array}{ll}1+x, & 0 \leq x \leq 2 \\ 3-x, & 2 < x \leq 3\end{array}\right.$.

If $f \circ f(x)$ is discontinuous at $a$ and $b$ in $[0,3]$ and $a