The inverse of the the function above is y = [tex] \sqrt{\frac{x+8}{2}} [/tex]
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.
[tex] \frac{x+8}{2} [/tex] = y^2 ----> Now take the square root of both sides.
[tex] \sqrt{\frac{x+8}{2}} [/tex] = y
What's left is your inverse. You can change the order so that it is in a more acceptable form.
y = [tex] \sqrt{\frac{x+8}{2}} [/tex]
