# Determine an equation of the inverse of y=(x-4)^2+5?

Aug 3, 2018

$y = 4 \pm \sqrt{x - 5}$

#### Explanation:

An inverse function can be found by swapping the $x$ and $y$

ie
$y = {\left(x - 4\right)}^{2} + 5$ is your original function

Swapping the $x$ and $y$ around, you'll get

$x = {\left(y - 4\right)}^{2} + 5$

Solving

$x = {\left(y - 4\right)}^{2} + 5$
$x - 5 = {\left(y - 4\right)}^{2}$
$\pm \sqrt{x - 5} = y - 4$
$y = 4 \pm \sqrt{x - 5}$