Question

Which equation is the inverse of y = 2x2 – 8?

Answer 1

The inverse of the the function above is y = $\sqrt{\frac{x+8}{2}}$

In order to find the inverse of any function, you need to switch the x and y values. Once you've done that, you need to solve for the new y value. The resulting equation will be your inverse. The work for this one is below.

y = 2x^2 - 8 ----> Switch the terms

x = 2y^2 - 8 ----> Add 8 to both sides.

x + 8 = 2y^2 ----> Divide both sides by 2.

$\frac{x+8}{2}$ = y^2 ----> Now take the square root of both sides.

$\sqrt{\frac{x+8}{2}}$ = y

What's left is your inverse. You can change the order so that it is in a more acceptable form.

y = $\sqrt{\frac{x+8}{2}}$