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:

`(1)/(7)x^2+3=y`

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

`y=f^(-1)(x)`

We get:

`(1)/(7)x^2+3=f^(-1)(x)`