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Math Help - Please help with domain of composite functions!

  1. #1
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    Please help with domain of composite functions!

    Hi everyone, I've been having trouble with finding the domain of composite functions. Can somebody please solve this problem for me? I think I have the answer but I'm not sure.
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  2. #2
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    Quote Originally Posted by gobbajeezalus View Post
    Hi everyone, I've been having trouble with finding the domain of composite functions. Can somebody please solve this problem for me? I think I have the answer but I'm not sure.
    The easiest way of getting the maximal domain is to get the rule for f(g(x)):

    f(g(x)) = \sqrt{g(x) - 16} = \sqrt{(5 - x) - 16} = \sqrt{-x - 11}. You should be able to get the maximal domain of this.
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  3. #3
    Super Member 11rdc11's Avatar
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    The domain of f(x) is x-16 \geq 0

    The domain of g(x) is all real numbers

    The domain of f(g(x)) = \sqrt{-x -11} is

    -x -11 \geq 0

    -x \geq 11

    x \leq -11

    Edit: posted to late
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