Answer
$f^{-1} (x)=-x-2$
The domain of the function $f$ is: $(-\infty, \infty)$.
The domain of the inverse of the function $f$ is: $[0, \infty)$.
Work Step by Step
We have $y=|x+2|=-x-2$
or, $x=-y-2$
or, $x+y=-2 \implies y=-x-2$
Replace $y$ with $f^{-1} (x)$.
so, $f^{-1} (x)=-x-2$
