Answer
The two functions are inverses to each other
Work Step by Step
$f(x) = \frac{x + 2}{x - 2}$
Find the inverse
$y = \frac{x + 2}{x - 2}$
y(x - 2) = x + 2
yx - 2y = x + 2
yx - x = 2 + 2y
x(y - 1) = 2 + 2y
$x = \frac{2 + 2y }{(y - 1)}$
$f^{-1}(x) = \frac{2 + 2x }{(x - 1)} = g(x)$
$g(x) = \frac{2x +2}{x - 1}$
Find the inverse
$y= \frac{2x +2}{x - 1}$
y(x - 1) = 2x + 2
yx - y = 2x + 2
yx - 2x = 2 + y
x(y - 2) = 2 + y
$x = \frac{2 + y}{y - 2}$
$g^{-1}(x) = \frac{2 + x}{x- 2} = f(x)$
The two functions are inverses to each other
