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Math Help - Domain of a function

  1. #1
    Member M670's Avatar
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    Domain of a function


    I am trying to figure out how to write the domain in interval notation
    i reduced the denominator to (x-4)^2 but am stuck now
    any help would be great

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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Domain of a function

    What you have said is not entirely correct, you can reduce the denominator to (x+4)^2 thus
    f(x) = \frac{x-2}{x^2+8x+16} = \frac{x-2}{(x+4)^2}

    For which value is the fraction not defined? i.e when is the denominator zero?
    Can you make a conclusion now?
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  3. #3
    Member M670's Avatar
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    Re: Domain of a function

    I believe the denominator is = to zero when x = to -4 or 4
    so in interval notation I got (infinity,-4) U (4, inifinity)
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Domain of a function

    Quote Originally Posted by M670 View Post
    I believe the denominator is = to zero when x = to -4 or 4
    so in interval notation I got (infinity,-4) U (4, inifinity)
    f(4) = \frac{4-2}{(4+4)^2} = \frac{2}{64} = \frac{1}{32}
    thus x=4 is not a problem. Only x=-4 is a problem because then the denominator will be equal to 0.

    Thus the domain is ... ?
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  5. #5
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    Re: Domain of a function

    correction ...

    (-\infty,-4) \cup (-4, \infty)

    only x = -4 is not in the domain.
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  6. #6
    Member M670's Avatar
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    Re: Domain of a function

    The domain is all real number excluding -4
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  7. #7
    MHF Contributor Siron's Avatar
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    Re: Domain of a function

    Quote Originally Posted by M670 View Post
    The domain is all real number excluding -4
    Exactly! \mathbb{R} \setminus \{-4\}
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  8. #8
    Member M670's Avatar
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    Re: Domain of a function

    Thank You to both of you
    I have been stuck on this for over a day now
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