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Math Help - Find the domain of each function

  1. #1
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    [solved] Find the domain of each function

    Book's kind of skimpy on this


    Find the domain of each function.

    f(x) = x / 3x - 1

    another one

    f(x) = 5x + 4 / x^2 + 3x + 2

    From how the book explains it, the only way I know to solve these is to plug random numbers in and see, but that's not exactly practical.

    Thank you for any help.
    Last edited by question111; January 30th 2009 at 11:49 AM.
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  2. #2
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    Hi

    A fraction is defined wherever the denominator is not equal to 0
    For the first one 3x-1=0 for x=1/3
    Therefore the domain is IR\{1/3}
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  3. #3
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    Thank you,

    I can see that x = 1/3 would make the denominator 0. Now that you point it out, it seems pretty obvious. However, how would I find that in problems where it's not so obvious?
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  4. #4
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    Let me clarify what I mean. Basically, I want to know how I can systematically work out the domain without just guessing what wouldn't work.

    It can be inferred just by looking at the first problem that the demoninator will be 0 if x = 1/3, but I really don't know what to do with the next problem. Is there something obvious I'm missing? Could someone work out the next problem, step-by-step?

    Maybe the next problem IS obvious just by looking to most of you, I dunno. Never been good in math. But suppose there were a problem that wasn't.
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  5. #5
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    Quote Originally Posted by question111 View Post
    Book's kind of skimpy on this


    Find the domain of each function.


    f(x) = 5x + 4 / x^2 + 3x + 2


    Thank you for any help.
    Hi question111,

    Like Running-gag told you, find out what makes the denominator = 0. Then the domain will be all real numbers except those values.

    x^2+3x+2=0

    (x+2)(x+1)=0

    x = -2 \ \ or \ \ x=-1

    So, the domain is all real numbers except -2 and -1.
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  6. #6
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    I understand. Thank you.
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