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

May 28, 2018

Consider $y = - 5 x + 2$

Our goal is to find the anti-image of x

$y - 2 = - 5 x$

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

Then the function inverse is $y = \frac{- x + 2}{5} = {f}^{- 1} \left(x\right)$

We can test the solution solving $f o {f}^{- 1}$

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

So $f o {f}^{- 1} = i \mathrm{de} n t i t y$ and ${f}^{- 1}$ is the inverse of $f$