Inverse of $$$y = x^{2} - 36$$$

Find the inverse of the function $$$y = x^{2} - 36$$$.

To find the inverse function, swap $$$x$$$ and $$$y$$$., and solve the resulting equation for $$$y$$$.

This means that the inverse is the reflection of the function over the line $$$y = x$$$.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: $$$y = x^{2} - 36$$$ becomes $$$x = y^{2} - 36$$$.

Now, solve the equation $$$x = y^{2} - 36$$$ for $$$y$$$.

$$$y = \sqrt{x + 36}$$$

$$$y = - \sqrt{x + 36}$$$

$$$y = \sqrt{x + 36}$$$A

$$$y = - \sqrt{x + 36}$$$A

Graph: see the graphing calculator.