Piecewise function

Question

x if −2≤x≤0;
x^2 if −2<x<0;
8-x. If if −2≤x≤3;
(d) Write down an analytic formula for f^{-1}, and state its domain and range.

Answer 1

Your pieces overlap. That is not the way to define a piecewise function.

Looks like your inverse function will also be piecewise, no? Just take the inverse on each piece.

Answer 2

There is a typo

8-x if 2≤x≤3