# How do you find the inverse of f(x)= 5x + 10?

Feb 14, 2016

The inverse of a function is the relation that is formed when the function is transformed over the line $y = x$

#### Explanation:

The inverse can be found algebraically by switching x for y and y for x in the equation. You must then isolate y.

$f \left(x\right) = 5 x + 10$

$y = 5 x + 10$

$x = 5 y + 10$

$x - 10 = 5 y$

$\frac{x - 10}{5} = y$

So, ${f}^{-} 1 \left(x\right) = \frac{x - 10}{5}$

Practice exercises:

1. Find the inverse of the following functions:

a) $f \left(x\right) = 3 x + 4$

b) $g \left(x\right) = \sqrt{4 x - 1}$

c) $h \left(x\right) = \frac{2}{2 x - 3}$

Good luck!