Question

For the function f(x) = √x/2, find f-1(x).

Answer 1

$\begin{gathered} f(x)=\frac{\sqrt[]{x}}{2} \\ \end{gathered}$

1. replace f(x) with y:

$\begin{gathered} y=\frac{\sqrt[]{x}}{2} \\ \end{gathered}$

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

$\begin{gathered} x=\frac{\sqrt[]{y}}{2} \\ \end{gathered}$

3. Solve for y:

$y=4x^2=(2x)^2$

4. replace y with f-1(x):

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