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

Answer 1

Julia Adams

#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!

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Answer 2

Jace Anderson

The domain of the function ( x^{1/3} ) is all real numbers, because any real number can be raised to the power of ( \frac{1}{3} ), including positive, negative, and zero values.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.