Question

Place the steps for finding f^-1(x) in the correct order

Answer 1

We are given the following function:

$f(x)=\sqrt[]{7x-21}$

We are asked to determine its inverse function:

$f^{-1}(x)$

To do that, we will do the following change:

$y=f(x)$

We get:

$y=\sqrt[]{7x-21}$

Now, since we want to determine the inverse we will swap variables, like this:

$x=\sqrt[]{7y-21}$

Now we will solve for "y", first by squaring both sides:

$x^2=7y-21$

Now we will add 21 to both sides:

$x^2+21=7y$

Now we will divide both sides by 7:

$\frac{1}{7}x^2+3=y$

This is the inverse function, therefore, we can do the following change:

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

We get:

$\frac{1}{7}x^2+3=f^{-1}(x)$