Question

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Answer 1

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 $f^{-1}(x)$ (read "f inverse of x"), we must interchange the values of x and y.

$y=2x^2-8$


The inverse is $x=2y^2-8$, but we want to simplify it by solving for y.

$x+8=2y^2 \\ \\ \frac{1}{2}x+4=y^2 \\ \\ y = +/- \sqrt{ \frac{1}{2}x+4 }$