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Math Help - domain

  1. #1
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    domain

    find the domain

    f(x)=sqrt{x^2/x^2-6x+8}
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by oneway1225 View Post
    find the domain

    f(x)=sqrt{x^2/x^2-6x+8}
    You require the solutions to \frac{x^2}{x^2 - 6x + 8} \geq 0.

    Case 1: Solve the simultaneous inequations x^2 \geq 0 AND x^2 - 6x + 8 > 0.

    Case 2: Solve the simultaneous inequations x^2 \leq 0 AND x^2 - 6x + 8 < 0.
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  3. #3
    MHF Contributor kalagota's Avatar
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    or easily, since what you want is

    \dfrac{x^2}{x^2-6x+8} = \dfrac{x^2}{(x-2)(x-4)} \geq 0

    you may want to create this table of signs..

    just complete the table.. and determine which interval do you need.. (i hope this is familiar to you.. )
    Attached Thumbnails Attached Thumbnails domain-table-signs.gif  
    Last edited by kalagota; December 24th 2008 at 07:21 AM.
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  4. #4
    Math Engineering Student
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    You don't have to consider x^2, since it's always positive, just analize the denominator.
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  5. #5
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Krizalid View Post
    You don't have to consider x^2, since it's always positive, just analize the denominator.
    yeah, thank mistake.. it should be positive.. thus the product below should be positive..
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