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

Question

asked Sep 1, 2023 159k views

1 Answer

Shunji Lin · Answer 1 · 2023-09-07T08:36:04+0000

We are given the following function:

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

We are asked to determine its inverse function:

To do that, we will do the following change:

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:

Now we will add 21 to both sides:

Now we will divide both sides by 7:

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

We get: