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

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Answer 1 · 2018-07-30T19:31:39

$x in RR$

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!

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