How can we composite two piecewise functions? Let say
$$f(x) := \left\{\begin{array}{l l}x+1 & \text{ if } -2\leq x<0 \\ x-1 & \text{ if }0\leq x\leq 2\end{array}\right.$$ 
How can we find out $f\circ f$? 

Hint: The first thing to do is to write down the domain and codomain of your function. Here we have:
\begin{equation}
f:[-2,2]\longrightarrow[-1,1]
\end{equation}
Next, since $[-1,1]\subset[-2,2]$, it is OK to compose $f$ with itself. Try to figure out yourself what $f\circ f$ does.
