#### Answer

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

#### Work Step by Step

$f(x) = 5x+2$
Let $f(x) = y$
$y = 5x+2$
Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse:
$x = 5y + 2$
$x - 2 = 5y$
$y = \frac{x-2}{y}$
$f^{-1}(x) = \frac{x-2}{y}$