Answer
$f^{-1} (x)=x+3$
Domain of the function $f$ is: $[4, \infty)$.
Domain of the inverse of function $f$ is: $[1,\infty)$.
Work Step by Step
We have $y=|x+4|+1=x-4+1=x-3$
To compute the inverse, we will have to interchange $x$ and $y$.
$x=y-3$
Re-write as: $ y=x+3$
Replace $y$ with $f^{-1} (x)$.
so, $f^{-1} (x)=x+3$
