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Math Help - Finding Domain and Range

  1. #1
    Newbie renae's Avatar
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    Finding Domain and Range

    What are the general rules for finding domain and range? Walk me through...

    Find Domain:

    f(x)= sqrt(4-x)/(x+1) (x^2+1)

    Find Range:

    f(x)= 5+sqrt(4-x)
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  2. #2
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    Quote Originally Posted by renae View Post
    What are the general rules for finding domain and range? Walk me through...

    Find Domain:

    f(x)= sqrt 4-x/(x+1) (x^2+1)
    \frac{\sqrt{4-x}}{(x+1)(x^2+1)}

    Now 4-x\geq 0 \mbox { and }x\not = -1.
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  3. #3
    Newbie renae's Avatar
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    Yeah, I know that, but how would I write it?
    I have down:

    (-inf, 4) U (4,0)

    which i know to be completely and utterly wrong, but I just get so confused on trying to write those.
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  4. #4
    MHF Contributor red_dog's Avatar
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    From 4-x\geq 0 we get x\leq 4 or x\in(-\infty,4].
    But x\neq -1 (else the denominator is 0).
    So, we must eliminate -1 from the interval.
    Then x\in(-\infty,4]-\{-1\} or x\in(-\infty,-1)\cup(-1,4]
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  5. #5
    MHF Contributor red_dog's Avatar
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    Quote Originally Posted by renae View Post
    Find Range:

    f(x)= 5+sqrt(4-x)
    \sqrt{4-x}\geq 0,\forall x\leq 4\Rightarrow 5+\sqrt{4-x}\geq 5,\forall x\leq 4
    Then the range is [5,\infty)
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