# How do you find the inverse of f(x) = 5x+2?

##### 1 Answer
Nov 2, 2017

Answer: ${f}^{- 1} \left(x\right) = \frac{x - 2}{5}$

#### Explanation:

Find the inverse of $f \left(x\right) = 5 x + 2$

Note that the inverse of a function can be found by flipping the $x$ and $y$ variables and solving for $y$. In this case, we can treat the $f \left(x\right)$ as a $y$, therefore:
$y = 5 x + 2$

Flipping the $x$ and $y$ variables, we have:
$x = 5 y + 2$

Solving for $y$:
$x = 5 y + 2$
$x - 2 = 5 y$
$y = \frac{x - 2}{5}$ or ${f}^{- 1} \left(x\right) = \frac{x - 2}{5}$ for inverse notation