Domain Question: Is X All Real?

  • Thread starter tysonk
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In summary: If C=1 then the domain would be all real numbers. If C=-1 then the domain would be all negative real numbers. Yep.
  • #1
tysonk
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I have a question about domain.
Let's say we have a function in the form of

y=(C/X)^0.5

Let's say for a particular case C = 0.

Is the domain of the function x cannot equal 0? Or is it all real?
 
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  • #2
tysonk said:
I have a question about domain.
Let's say we have a function in the form of

y=(C/X)^0.5

Let's say for a particular case C = 0.

Is the domain of the function x cannot equal 0? Or is it all real?
[RANT]
The idea of Domain is something that is explained really, really poorly in Calc classes and below. When you or someone else asks this question:

What is the domain of f(x)?

what they mean is:

What is the largest subset, S, of R such that if x is in S, f(x) is defined?

Once you get past calculus classes, when someone says "I have this function f" they state explicitly what the domain is.
[/RANT]


Anyway, to answer your question, you need to determine at which points of R, the quotient (0/x)^(1/2) is defined. What makes you think that 0 is not in the domain of f?
 
  • #3
Because we have (0/0)^0.5
 
  • #4
tysonk said:
Because we have (0/0)^0.5

Correct. But, consider two things: 1)If C wasn't 0 would (C/0)^.5 be defined?

2)Is x=0 the only value of x for which (C/x)^.5 is not defined?
 
  • #5
1) No, it wouldn't.

2) well x can't be negative, but since we have zero in the numerator I think x can also include negative reals in this case.
 
  • #6
tysonk said:
1) No, it wouldn't.

2) well x can't be negative, but since we have zero in the numerator I think x can also include negative reals in this case.

You are correct, since the division is inside the parenthesis, the entire real line, with the exception of 0, is killed by the 0/x. So, putting this together, what is the domain of f when C=0?
 
  • #7
All real numbers except for 0.
 
  • #8
tysonk said:
All real numbers except for 0.

Yep. Now, what if C=1 and what if C=-1?
 

1. What does it mean for something to be "real"?

The concept of "real" can vary depending on the context. In science, something is considered real if it can be observed or measured through empirical evidence. This means that it has a physical existence and can be verified through experimentation or observation.

2. How can we determine if X is all real?

Determining if X is all real requires a thorough examination and analysis of the evidence. This can include conducting experiments, collecting data, and consulting with other experts in the field. It is important to consider multiple perspectives and gather as much evidence as possible to make an informed conclusion.

3. Is there a difference between something being "real" and something being "true"?

Yes, there is a distinction between these two concepts. In science, something can be considered "real" if it exists in the physical world, but it may not necessarily be true. Truth is often subjective and can be influenced by personal beliefs or biases. In order to determine if something is true, it must be supported by evidence and withstand rigorous testing and scrutiny.

4. Can something be partially real?

In science, there is no concept of something being partially real. Either something exists in the physical world and can be observed or measured, or it does not. However, there are cases where something may appear to be real based on current evidence, but further research and evidence may change our understanding of its existence.

5. What is the significance of knowing if X is all real?

Determining if X is all real can have significant implications in various fields, such as medicine, technology, and environmental studies. It can help us better understand the world around us and make informed decisions based on evidence. It can also lead to advancements and breakthroughs in scientific research and contribute to our overall knowledge and understanding of the universe.

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