Question

F (x) = ^3 square root x- 15. Find the inverse of f(x).

Answer 1

Given the function

`f(x)=\sqrt[3]{x-15}`

we want to find the its inverse function

`f^(-1)(x).`

In order to do that, we will replace f(x) with y. This is done to make the rest of the process easier. So, we have

`y=\sqrt[3]{x-15}`

Now, let's replace every x with a y and every y with an x,

`x=\sqrt[3]{y-15}`

and we must solve this equation for y. Then, by raising both sides to the third power, we get

`x^3=y-15`

and by adding 15 to both sides, we have

`\begin{gathered} x^3+15=y \\ or\text{ equivalently,} \\ y=x^3+15 \end{gathered}`

Finally, by replacing y with f^-1(x), we have

`f^(-1)(x)=x^3+15`

Therefore, the answer is option C.