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Math Help - Inverse functions

  1. #1
    Senior Member
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    Jul 2008
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    Angry Inverse functions

    Hi

    I've been trying to prove these pair of functions are inverses:

    f(x) = sqrt(16-x^2) and g(x) = -sqrt(16-x^2)

    using f(g(x)) = g(f(x)) = x

    however when I do the working out it seems i get f(g(x)) = abs(x) BUT g(f(x)) = -abs(x) for some reason. I just did basic substitution n I've checked a few times but I can't seem to resolve this problem.

    Could someone please help?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by xwrathbringerx View Post
    Hi

    I've been trying to prove these pair of functions are inverses:

    f(x) = sqrt(16-x^2) and g(x) = -sqrt(16-x^2)

    using f(g(x)) = g(f(x)) = x

    however when I do the working out it seems i get f(g(x)) = abs(x) BUT g(f(x)) = -abs(x) for some reason. I just did basic substitution n I've checked a few times but I can't seem to resolve this problem.

    Could someone please help?
    Your work is correct. They two expressions do not satisfy the test for being inverses. Start with f(x) and switch the x's and y's. Solve for y again. If g(x) was the inverse of f(x), you would end up with g(x) but you don't.
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