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Math Help - Composition of functions

  1. #1
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    Composition of functions

    find the composition of f with g and state the domain..

    f(x)=(x-3)^(1/2), g(x)=(x^2+3)^(1/2)

    tenQ
    Last edited by mr fantastic; March 1st 2010 at 01:57 AM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by redcherry View Post
    find the composition of f with g and state the domain..

    f(x)=(x-3)^(1/2), g(x)=(x^2+3)^(1/2)

    tenQ
    What have you tried and where are you stuck?
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  3. #3
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    tq~

    f(g(x))=f((x^2+3)^(1/2))
    =((x^2+3)^(1/2)-3)^(1/2))

    i stuck at here..
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  4. #4
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    Quote Originally Posted by redcherry View Post
    f(g(x))=f((x^2+3)^(1/2))
    =((x^2+3)^(1/2)-3)^(1/2))

    i stuck at here..
    Okay, you've found the composition so the only thing left to do is state the domain! The only "problem" appears to be square roots. Obviously x^2+ 3 is never negative so your only condition is that you must have (x^2+3)^{1/2}\ge 3. What values of x satisfy that?


    The equation (x^2+3)^{1/2}= 3 gives values of x that separate "<" from ">". Find those and determine which of the intervals separated by those values satisfy the inequality.
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