Verified Answer :

Blitztiger

To get the inverse, we should swap the x- and y-variables, then solve for y. Swapping the variables gives the equation: \(x=2y^2-8\)
Solving for y:
\(x+8=2y^2 \\ \frac{x+8}{2}=y^2 \\ y=\sqrt{\frac{x+8}{2}}\)

Step-by-step explanation:

In order to get the inverse of equation, we will interchange the variables and solve for x and y as follows.

             \(y = 2x^{2} - 8\)

whereas,  \(y + 8 = 2x^{2}\)

    or              x = \(\sqrt{\frac{y+8}{2}}\)

Now, on interchanging the variable we will get the equation as follows.

               \(x = 2y^{2} - 8\)

               \(x + 8 = 2y^{2}\)

                     y = \(\sqrt{\frac{x+8}{2}}\)