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Math Help - Answering domain

  1. #1
    Senior Member Paze's Avatar
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    Answering domain

    Hi MHF.

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

    Do I say:

    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!
    Last edited by Paze; October 11th 2013 at 02:33 AM.
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  2. #2
    MHF Contributor
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    Re: Answering domain

    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.
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  3. #3
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    Re: Answering domain

    Quote Originally Posted by Paze View Post
    Hi MHF.

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

    Do I say:

    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|
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  4. #4
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    Re: Answering domain

    Quote Originally Posted by votan View Post
    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.

    Quote Originally Posted by votan View Post
    I would write x neq |1|
    You must mean |x| ≠ 1.
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  5. #5
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    Re: Answering domain

    Quote Originally Posted by emakarov View Post
    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.

    You must mean |x| ≠ 1.
    I started typing before you posted your reply, otherwise I wouldn't have.

    I agree on your observation for x ≥ 0 But I tend to write it by the principle of the least action.

    Good catch |x| ≠ 1
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