# How do you find the inverse of  f(x) = x^2 + 9?

Dec 26, 2015

$\textcolor{w h i t e}{\times} {f}^{-} 1 \left(x\right) = \sqrt{x - 9}$

#### Explanation:

$\textcolor{w h i t e}{\times} f \left(x\right) = {x}^{2} + 9$

$\textcolor{w h i t e}{\times} y = {x}^{2} + 9$
$\implies y \textcolor{red}{- 9} = {x}^{2} + 9 \textcolor{red}{- 9}$
$\implies \sqrt{{x}^{2}} = \sqrt{y - 9}$

$\implies {f}^{-} 1 \left(x\right) = \sqrt{x - 9}$