What is the domain for variables with cube roots?

  • MHB
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In summary, the domain for the first equation is all real numbers, while the domain for the second equation is any real number. This is because the cube root of any real number can be either positive or negative.
  • #1
mathdad
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Specify the domain of each variable.

1. ax + b

Here x can be any integer.

In that case the domain is R, where R is ALL REAL NUMBERS.

2. ax^(1/3) + b

Let x^(1/3) be the cube root of x.

Let D = domain

x^(1/3) is > or = 0

[x^(1/3)]^3 > or = 0^(1/3)

x > or = 0

D = {x| x > or = 0}

Is any of this right?
 
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  • #2
RTCNTC said:
Specify the domain of each variable.

1. ax + b

Here x can be any integer.

In that case the domain is R, where R is ALL REAL NUMBERS.

Correct, there would be no restriction we would need to impose on $x$.

RTCNTC said:
2. ax^(1/3) + b

Let x^(1/3) be the cube root of x.

Let D = domain

x^(1/3) is > or = 0

[x^(1/3)]^3 > or = 0^(1/3)

x > or = 0

D = {x| x > or = 0}

Is any of this right?

Let's think about this...what is the cube of a negative number?
 
  • #3
Negative numbers can't have real number square roots, but negative numbers can have real number cube roots.

Sample: (-8)^(1/3) = -2

Back to my question.

(x)^(1/3) is the cube root of x. The domain can be any real number.
 

FAQ: What is the domain for variables with cube roots?

What is the meaning of "Specify the Domain"?

"Specify the Domain" refers to a process in which scientists or researchers define the scope or boundaries of their study. It involves identifying the specific subject or topic that will be investigated and setting limits on what will be included and excluded from the study.

Why is it important to specify the domain in scientific research?

Specifying the domain is important because it helps to clarify the focus of the research and ensure that the study remains relevant and manageable. It also allows other researchers to understand the context of the study and potentially replicate or build upon the findings.

How do scientists go about specifying the domain?

Scientists often use a combination of literature review, consultation with experts in the field, and defining key research questions to specify the domain. They may also consider any constraints or limitations, such as time or resources, that may impact the scope of their study.

What are some common mistakes scientists make when specifying the domain?

One common mistake is being too broad or vague with the domain, which can lead to a lack of focus and difficulty in drawing meaningful conclusions. Another mistake is being too narrow and excluding important factors that could impact the results of the study.

Can the domain change during the course of a study?

Yes, the domain can change if new information or unexpected findings arise during the research process. However, any changes should be carefully considered and clearly communicated to ensure the validity and integrity of the study.

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