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

Apr 17, 2015

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

$y = {x}^{3}$

$x = {y}^{\frac{1}{3}}$

$\therefore {f}^{-} 1 \left(x\right) = \sqrt[3]{x}$

Step 2. Now let's take a look at the graph of ${f}^{-} 1 \left(x\right) = \sqrt[3]{x}$

What we can see below is the fact that x can be an element of a real number ($x E \mathbb{R}$ - which is the domain of this inverse function), and that ${f}^{-} 1 \left(x\right)$ can also be an element of a real number
(${f}^{-} 1 \left(x\right) E \mathbb{R}$ - which is the range of this inverse function).

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