Answer
$f^{-1}(x) = \frac{x-3}{x-1}$
Work Step by Step
$f(x) = \frac{x-3}{x-1}$
Let $f(x) = y$
$y = \frac{x-3}{x-1}$
$x = \frac{y-3}{y-1}$
$xy - x = y-3$
$xy - y = x - 3$
$y(x -1) = x-3$
$y = \frac{x-3}{x-1}$
$f^{-1}(x) = \frac{x-3}{x-1}$