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

1 Answer
Jul 30, 2018

Answer:

#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!