Question

How do you find the inverse of `f(x)=root3x`?

Answer 1

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

Explanation:

We have: `f(x) = root(3)(x)`

Let's replace `f(x)` with `y`:

`Rightarrow y = root(3)(x)`

Interchanging variables:

`Rightarrow x = root(3)(y)`

We must now solve the equation for `y`:.

Cubing both sides of the equation:

`Rightarrow (x)^(3) = (root(3)(y))^(3)`

`Rightarrow x^(3) = y`

`Rightarrow y = x^(3)`

Now, let's replace `y` with `f^(- 1)(x)`:

`therefore f^(- 1)(x) = x^(3)`