Answer
$(-\infty,5)\cup(5,\infty)$
Work Step by Step
We are given the function:
$f(x)=\dfrac{1}{x-5}$
We graph the function.
The domain of $f$ is $(-\infty,5)\cup(5,\infty)$.
The range of $f$ is $(-\infty,0)\cup(0,\infty)$.
Using the Horizontal Line Test we notice that any horizontal line (except $y=0$) intersects the graph in one point. Therefore the function $f$ has an inverse on $(-\infty,5)\cup(5,\infty)$.
