Domain Question: Is X All Real?

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Homework Help Overview

The discussion revolves around determining the domain of a function defined as y=(C/X)^0.5, particularly when C is set to 0. Participants are exploring the implications of this setup on the values that x can take.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the definition of the domain and whether x can equal 0 or if it must be excluded. There is also exploration of how the value of C affects the domain, particularly in cases where C is 0, 1, or -1.

Discussion Status

There is an active exploration of the domain with participants providing reasoning and counterpoints. Some have suggested that the domain excludes 0, while others are considering the implications of different values for C. The discussion is ongoing with no explicit consensus reached yet.

Contextual Notes

Participants note that the concept of domain is often poorly explained in calculus classes, which may contribute to the confusion surrounding the question. There is also mention of the need for clarity on what constitutes the domain in different scenarios.

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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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?
 
Because we have (0/0)^0.5
 
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?
 
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.
 
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?
 
All real numbers except for 0.
 
tysonk said:
All real numbers except for 0.

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

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