Question

What is the domain of `x^(1/3)`?

Answer 1

`x in RR`

Explanation:

The domain is the set of `x` values that make this function defined. We have the following:

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

Is there any `x` that will make this function undefined? Is there anything that we cannot raise to the one-third power?

No! We can plug in any value for `x` and get a corresponding `f(x)`.

To make this more tangible, let's plug in some values for `x`:

`x=27=>f(27)=27^(1/3)=3`

`x=64=>f(64)=64^(1/3)=4`

`x=2187=>f(2187)=2187^(1/3)=7`

`x=5000=>f(5000)=5000^(1/3)~~17.1`

Notice, I could have used much higher `x` values, but we got an answer each time. Thus, we can say our domain is

`x inRR`, which is just a mathy way of saying `x` can take on any value.

Hope this helps!