Find the inverse of $f(x) = \frac{x - 6}{x - 5}$ and determine its domain and range.
(For the domain and range, give your answer as an interval in the form (*,*). Use the symbol $\infty$ for infinity, $\cup$ for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter $\emptyset$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)
$f^{-1}(x) = $
domain of $f^{-1}(x)$:
range of $f^{-1}(x)$: