To find the inverse of a function, we find the function that reverses it. That means that for an input x and output y in a function, its inverse would have input y and output x.
For [tex]f^{-1}(x)[/tex] (read "f inverse of x"), we must interchange the values of x and y.
[tex]y=2x^2-8[/tex]
The inverse is [tex]x=2y^2-8[/tex], but we want to simplify it by solving for y.
[tex]x+8=2y^2 \\ \\ \frac{1}{2}x+4=y^2 \\ \\ y = +/- \sqrt{ \frac{1}{2}x+4 } [/tex]
