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Math Help - Solving equations involving inverse function (gf)^-1

  1. #1
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    [SOLVED] Solving equations involving inverse function (gf)^-1

    The functions f and g are defined by

    f(x) = (1-x)/(2-x), x >2 and
    g(x) = xlnx (x more than or equals to 1)

    f^-1(x) is (2x-1)(x-1).

    Solve exactly the equation (gf)^-1(x) = 3.

    What I've got:
    gf (x) = ((1-x)/(2-x)) ln ((1-x)/(2-x))
    But I can't make x the subject.

    Or, (gf)^-1 = f^-1g^-1 . So find g^-1 first and then f^-1.


    But I can't find g^-1. I'm stuck.

    The answer is x = 2ln2, but I can't seem to get it. Can someone please help me out here? I've been trying for ages. Thanks!
    Last edited by thesocialnetwork; June 10th 2011 at 07:05 AM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    (g\circ f)^{-1}(x)=3\Leftrightarrow x=(g\circ f)(3) so, x=(g\circ f)(3)=\ldots=2\log 2 .
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  3. #3
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    thanks!!
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by thesocialnetwork View Post
    thanks!!

    You are welcome!
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