# What is the inverse of h(x) = 5x + 2?

Jul 30, 2016

$y = \frac{1}{5} x - \frac{2}{5}$

#### Explanation:

We have

$y = 5 x + 2$

When we invert a function what we are doing is reflecting it across the line $y = x$ so what we do is swap the x and y in the function:

$x = 5 y + 2$

$\implies y = \frac{1}{5} x - \frac{2}{5}$

Jul 30, 2016

The inverse of a function $h \left(x\right)$ is a function $f$ such that the composition $h \left(f\right) = i \mathrm{de} n t i t y$ or, in other words, such that $h \left(f \left(x\right)\right) = x$

#### Explanation:

Given this definition, we apply $h$ in the point $f \left(x\right)$; so $h \left(f \left(x\right)\right) = 5 f \left(x\right) + 2$. But this must be $h \left(f \left(x\right)\right) = 5 f \left(x\right) + 2 = x$ and hence $5 \left(f \left(x\right)\right) = x - 2$, and then $f \left(x\right) = \frac{x - 2}{5} = \frac{1}{5} x - \frac{2}{5}$