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Math Help - How can I find the domain of this function?

  1. #1
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    How can I find the domain of this function?

    f(x) = (√1-2x)/(x^2 -9) + 3/(x^2 - 6x +8)


    I thought:


    x^2-9 -> (x-3)(x+3)


    x^2-6x+8 -> (x-4)(x-2)




    (√1-2x) (x-4)(x-2) + 3(x-3)(x+3)
    ---------------------------------------
    (x-3)(x+3)(x-4)(x-2)


    I just don't know what to do next and it just feels not right , please someone tell me how can I find the domain.
    Last edited by letranger9000; October 29th 2013 at 04:49 PM.
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  2. #2
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    Re: How can I find the domain of this function?

    Hello, letranger9000!

    Find the domain of: . f(x) \;=\;\frac{\sqrt{1-2x}}{x^2 -9} + \frac{3}{x^2 - 6x +8}

    I thought:

    x^2-9 \:=\:(x-3)(x+3)

    x^2-6x+8 \:=\:(x-4)(x-2) . Good!

    The denominators must not be zero.
    . . Hence: . x \:\ne\:-3, 2, 3, 4

    From that radical: . 1-2x \:\ge\:0 \quad\Rightarrow\quad -2x \:\ge\:-1
    . . Hence: . x \:\le\:\tfrac{1}{2}


    We want all numbers less than or equal to \tfrac{1}{2}, except -3.

    Domain: . (\text{-}\infty,\,\text{-}3) \,\cup\,\left(\text{-}3,\,\tfrac{1}{2}\right]
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