# What is the inverse of f(x)=pi*arccos(x-1)+1?

$y = \cos \left(\frac{x - 1}{\pi}\right) + 1$

#### Explanation:

$y = \pi \arccos \left(x - 1\right) + 1$

To take an inverse, you switch the x and y in this equation and solve for y:

$x = \pi \arccos \left(y - 1\right) + 1$

$\frac{x - 1}{\pi} = \arccos \left(y - 1\right)$

$\cos \left(\frac{x - 1}{\pi}\right) = \cos \left(\arccos \left(y - 1\right)\right)$

$\cos \left(\frac{x - 1}{\pi}\right) = y - 1$

$y = \cos \left(\frac{x - 1}{\pi}\right) + 1$
Solved!