Question

If f(x) = x2 -1, what is the equation for f1(x)?

Answer 1

$f(x)=x^2-1$

1. First, replace f(x) with y

$y=x^2-1$

2. Replace every x with a y and replace every y with an x.

$x=y^2-1$

3. solve for y:

$\begin{gathered} y^2=x+1 \\ y=\pm\sqrt[]{x+1} \end{gathered}$

4. Replace y with f−1(x):

$f^{-1}(x)=\pm\sqrt[]{x+1}$