Question

How do you find the domain and range of the inverse of the given function `f(x) = x^3`?

Answer 1

Step 1. Let's find the inverse function of the given function.

`y=x^3`

`x=y^(1/3)`

`:. f^-1(x)=root(3)x`

Step 2. Now let's take a look at the graph of `f^-1(x)=root(3)x`

What we can see below is the fact that x can be an element of a real number (`xERR` - which is the domain of this inverse function), and that `f^-1(x)` can also be an element of a real number
(`f^-1(x)ERR` - which is the range of this inverse function).

graph{y=root(3)x [-10, 10, -5, 5]}