Answer
See graph and explanations.
Work Step by Step
Step 1. Graph the piece-wise function as shown in the first figure.
Step 2. To evaluate $f(f(x))$, use the values of $f(x)$ as input for the composite. We can see that in the interval of $x\in[-3,2]$, $f(x)\in [-1,1]$ which gives $f(f(x))=-1$ based on the piece-wise function.
Step 3. In the interval of $x\in[-4,-3]$, $f(x)\in [1,2]$ which gives $f(f(x))=(-x-2)-2=-x-4$ based on the piece-wise function.
Step 4. Plot $f(f(x))$ based on the above results as shown in the second figure.
