$h$ doesn't have an inverse.
Work Step by Step
We are given the function: $h(x)=|x+1|-1$ Graph the function using a set of points: $x=-3\Rightarrow h(-3)=|-3+1|-1=1$ $x=-2\Rightarrow h(-2)=|-2+1|-1=0$ $x=-1\Rightarrow h(-1)=|-1+1|-1=-1$ $x=0\Rightarrow h(0)=|0+1|-1=0$ $x=1\Rightarrow h(1)=|1+1|-1=1$ Graph the function. Perform the Horizontal Line Test. The test fails as there are horizontal lines which intersect the graph at more than one point. Therefore, the function doesn't have an inverse.