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Math Help - [SOLVED] Domain vs Range problem

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    Question [SOLVED] Domain vs Range problem

    Range/Domain Problem

    so question goes something like this ...

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

    and i am asked for the range of f^-1(g(y))

    i worked out f^-1(g(y)) to be: e^((1/g(y))-1)

    now this is defined provided the range of g(y) is a subset of the Domain of f^-1

    for this to be true, the Range of g(y) must be restricted to (0, 2] {as opposed to the [0,2] it was before}

    now this is the step i do not understand... my answer book says that therefor the range of f^-1(g(y)) is [e^-1/2,∞)

    can any1 please explain to me the last step?

    thanks
    Last edited by XonBugeja; April 30th 2010 at 12:17 PM. Reason: Scratch that.. just figured it out XD
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