# How do you find the inverse of f(x) = (3x + 4) / 5?

Jul 14, 2017

You have $y = \frac{3 x + 4}{5}$

To find ${f}^{- 1} \left(x\right)$ you switch the $x$s and $y$s.

$y = \frac{3 x + 4}{5}$ becomes $x = \frac{3 y + 4}{5}$

$5 x = \frac{5 \left(3 y + 4\right)}{5} = 3 y + 4$

$5 x - 4 = 3 y + 4 - 4 = 3 y$

$\frac{5 x - 4}{3} = \frac{3 y}{3} = y$