Domain Question: Is X All Real?

[tysonk]

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?

 

[Robert1986]

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?

 

[tysonk]

Because we have (0/0)^0.5

 

[Robert1986]

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?

 

[tysonk]

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.

 

[Robert1986]

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?

 

[tysonk]

All real numbers except for 0.

 

[Robert1986]

All real numbers except for 0.

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