# How do you find the inverse function of the function f(x) = -3x + 2?

Aug 1, 2016

$\text{the inverse of function is :} {f}^{'} \left(x\right) = \frac{2 - x}{3}$

#### Explanation:

$\text{approach 1:}$

$f \left(x\right) = y = - 3 x + 2$

$3 x = 2 - y$

$x = \frac{2 - y}{3}$

$\text{now ; x and y mutually changed}$

$y = \frac{2 - x}{3}$

${f}^{'} \left(x\right) = \frac{2 - x}{3}$

$\text{approach 2: use the formula :}$

$f \left(x\right) = \frac{a x + b}{c x + d} \text{ ; } {f}^{'} \left(x\right) = \frac{- d x + b}{c x - a}$

$a = - 3 \text{ ; "b=2" ; "c=0" ; } d = 1$

${f}^{'} \left(x\right) = \frac{- x + 2}{0 \cdot x + 3}$

${f}^{'} \left(x\right) = \frac{2 - x}{3}$