# Math Help - Answering domain

Hi MHF.

When giving an answer for a domain, say for: $f(x)=\sqrt{x}$

Do I say:

$D(f)=R | x \geq 0" alt="D(f)=R | x \geq 0" />

Well...Tex codes aren't cooperating..I'll try and write it:

D(f)=R|x is greater than or equal to 0

Or do I write:

D(f)=x is a part of R
| x is greater than or equal to 0

Which method is correct?

Also, when I have multiple values where x is not defined, but these values do not lie on a range such as the case for: $f(x)=\frac{x}{x^2-1}$

How do I answer for -1 and 1? Do I write:

D(f)=R
|x is not equal to -1, x is not equal to 1 ?

Thanks!

The first part of the set-builder notation is a variable or an expression containing a variable, possibly followed by "∈ A" for some set A. The second part is some property of the variable. So, the correct notations are $\{x\in\mathbb{R}\mid x\ge0\}$ and $\{x\in\mathbb{R}\mid x\ne-1\text{ and }x\ne1\}$.

Hint: In LaTeX, use \mid to write the middle vertical bar because it creates correct spaces around it.

Originally Posted by Paze
Hi MHF.

When giving an answer for a domain, say for: $f(x)=\sqrt{x}$

Do I say:

$D(f)=R | x \geq 0" alt="D(f)=R | x \geq 0" />

Well...Tex codes aren't cooperating..I'll try and write it:

D(f)=R|x is greater than or equal to 0

Or do I write:

D(f)=x is a part of R
| x is greater than or equal to 0

Which method is correct?

Also, when I have multiple values where x is not defined, but these values do not lie on a range such as the case for: $f(x)=\frac{x}{x^2-1}$

How do I answer for -1 and 1? Do I write:

D(f)=R
|x is not equal to -1, x is not equal to 1 ?

Thanks!
I would write it as simple as x>=0

I would write x neq |1|

Originally Posted by votan
I would write it as simple as x>=0
If the question asks to write a set, this answer would be incorrect because x ≥ 0 is a property, not a set. But, of course, it is clear what is intended.

Originally Posted by votan
I would write x neq |1|
You must mean |x| ≠ 1.