Inverse of $$$y = 5 x^{2} + 10$$$

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: $$$y = 5 x^{2} + 10$$$ becomes $$$x = 5 y^{2} + 10$$$.

Now, solve the equation $$$x = 5 y^{2} + 10$$$ for $$$y$$$.

$$$y = \sqrt{5} \sqrt{x - 10}$$$

$$$y = - \sqrt{5} \sqrt{x - 10}$$$

$$$y = \sqrt{5} \sqrt{x - 10}$$$A

$$$y = - \sqrt{5} \sqrt{x - 10}$$$A

Graph: see the graphing calculator.