Inverse of $$$y = 2 x^{2} - 4$$$

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: $$$y = 2 x^{2} - 4$$$ becomes $$$x = 2 y^{2} - 4$$$.

Now, solve the equation $$$x = 2 y^{2} - 4$$$ for $$$y$$$.

$$$y = \sqrt{2} \sqrt{x + 4}$$$

$$$y = - \sqrt{2} \sqrt{x + 4}$$$

$$$y = \sqrt{2} \sqrt{x + 4}$$$A

$$$y = - \sqrt{2} \sqrt{x + 4}$$$A

Graph: see the graphing calculator.