The inverse of the function is y = [tex] \sqrt{\frac{x - 2}{2}} [/tex]
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
[tex] \frac{x-2}{2} [/tex] = y^2 ---> take the square root of both sides.
[tex] \sqrt{\frac{x - 2}{2}} [/tex] = y
