Let f(x)

$f(x)= \begin{cases}1+x, & 0 \leq x \leq 2 \\ 3-x, & 2

It can be written as,

$f(x)=\left\{\begin{array}{c}1+x, 0 \leq x \leq 1 \\ 1+x, 1

When, $0 \leq x \leq 1$

Now when, $0 \leq x \leq 1$ then, $1 \leq x+1 \leq 2$

When, $1

Now when, $1

When, $2

Now when , $2

$f(f(x))=\left\{\begin{array}{l}2+x, 0 \leq x \leq 1 \\ 2-x, 1