Answer
See graph and explanations.
Work Step by Step
Step 1. Graph the piece-wise function as shown in the first figure.
Step 2. For $x\in[-2,-1]$, $f(x)\in[-1,0]$, thus $f(f(x))=(x+1)+1=x+2$
Step 3. For $x\in[-1,0)$, $f(x)\in[0,1)$, thus $f(f(x))=(x+1)-1=x$
Step 4. For $x\in[0,1]$, $f(x)\in[-1,0]$, thus $f(f(x))=(x-1)+1=x$
Step 5. For $x\in[1,2)$, $f(x)\in[0,1]$, thus $f(f(x))=(x-1)-1=x-2$
Step 6. Graph the composite $f(f(x))$ based on the above results as shown in the second figure.
