Inverse of $$$y = x^{2} - 10 x$$$

Find the inverse of the function $$$y = x^{2} - 10 x$$$.

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: $$$y = x^{2} - 10 x$$$ becomes $$$x = y^{2} - 10 y$$$.

Now, solve the equation $$$x = y^{2} - 10 y$$$ for $$$y$$$.

$$$y = \sqrt{x + 25} + 5$$$

$$$y = 5 - \sqrt{x + 25}$$$

$$$y = \sqrt{x + 25} + 5$$$A

$$$y = 5 - \sqrt{x + 25}$$$A

Graph: see the graphing calculator.