# How do you find the inverse of  f(x) = (x + 2)^2 and is it a function?

Jul 20, 2016

${f}^{-} 1 \left(x\right) = \sqrt{x} - 2$

The inverse is a function.

#### Explanation:

Find the inverse by switching $x$ and $y$ and solving for $y$.

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

Switch $x$ and $y$.

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

Solve for $y$. Begin by taking the square root of both sides. Note that taking the square root of something squared is that number ($\sqrt{{x}^{2}} = x$).

$\sqrt{x} = \sqrt{{\left(y + 2\right)}^{2}}$

$\sqrt{x} = y + 2$

$\sqrt{x} - 2 = y$

$y = \sqrt{x} - 2$

The inverse of $y = {\left(x + 2\right)}^{2}$ is:

${f}^{-} 1 \left(x\right) = \sqrt{x} - 2$

The graph of the inverse takes the form of what follows:

graph{sqrt(x)-2 [-10, 10, -5, 5]}

The inverse is a function.