#### Answer

$f^{-1}(x) = \frac{2x + 2}{1 - x}$

#### Work Step by Step

$f(x) = \frac{x - 2}{x + 2}$
$y = \frac{x - 2}{x + 2}$
y(x + 2) = x - 2
yx + 2y = x - 2
2y + 2 = x - yx
2y + 2 = x( 1 - y)
$x = \frac{2y + 2}{1 - y}$
$f^{-1}(x) = \frac{2x + 2}{1 - x}$