Question

Find the inverse of the function y=2x^2+2

Answer 1

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

In order to find this, you must start by switching the y and x values. Once you do this, you can solve for the new y value and that will be in inverse. The work is done for you below.

y = 2x^2 + 2 ---> switch x and y

x = 2y^2 + 2 ---> subtract 2 from both sides

x - 2 = 2y^2 ---> divide both sides by 2

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

$\sqrt{\frac{x - 2}{2}}$ = y