Question

If the function fis defined by f(x) = x ^ 5 - 1 then the inverse, f ^ - 1 is defined by f ^ - 1 * (x) =

Answer 1

Given the function:

`f(x)=x^5-1`

We have that f(x) = y, so:

`y=x^5-1`

Substitute x with y:

`x=y^5-1`

And solve for y:

`\begin{gathered} x+1=y^5-1+1 \\ x+1=y^5 \\ y=\sqrt[5]{x+1} \end{gathered}`

Answer:

`\sqrt[5]{x+1}`