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Thread: Composition of Functions

  1. #1
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    Post Composition of Functions

    Hello everyone,

    I'm having trouble finding the sums of functions.

    My particular problem is,

    f(x)=radical(x2-4) ; g(x)=x2/x2+1

    They're asking me to solve (f+g)(x).

    If (f+g)(x) is the same thing as f(x)+g(x) then:
    radical(x2-4)+x2/x2+1
    (x-2)+?

    Can x2/x2+1 be simplified so I can add the two functions easier?

    I tried simplifying a bunch of things but I can't seem to get anywhere.
    Any help would be appreciated. Thanks in advance!
    Last edited by badonm; Sep 14th 2008 at 04:03 PM.
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  2. #2
    MHF Contributor
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    (f+g)(x) = f(x) + g(x)

    (f \circ g)(x) = f[g(x)]
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  3. #3
    Super Member 11rdc11's Avatar
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    I'm not sure how your functions look but I'm going to assume it was like this and you just forgot to indicate it was up to a power. Correct me if I'm wrong.

    f(x)=\sqrt{x^2-4}

    g(x)=\frac{x^2}{x^2+1}

    so

    (f+g)(x) = f(x) + g(x)

    = \sqrt{x^2-4} + \frac{x^2}{x^2+1}

    find common denominator

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