Answer
$f^{-1}(x) = 5x - 3$
Work Step by Step
$f(x) = \frac{1}{5}x + \frac{3}{5}$
Let $f(x) = y$:
$y = \frac{1}{5}x + \frac{3}{5}$
Switch the variables $x$ and $y$ to find the inverse and solve for $y$:
$x = \frac{1}{5}y + \frac{3}{5}$
$x = \frac{y}{5} + \frac{3}{5}$
$x-\frac{3}{5} = \frac{y}{5} $
$5x - \frac{15}{5} = y$
$y = 5x - 3$
$f^{-1}(x) = 5x - 3$
