Answer
$f^{-1} (x)=-x-1$
Domain of the function $f$ is: $[1, \infty)$.
Domain of the inverse of function $f$ is: $(-\infty,-2]$.
Work Step by Step
We have $y=-|x-1|-2=-(x-1)-2=-x-1$
To compute the inverse, we will have to interchange $x$ and $y$.
$x=-y-1$
Re-write as: $ y=-x-1$
Replace $y$ with $f^{-1} (x)$.
so, $f^{-1} (x)=-x-1$
