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Thread: [SOLVED] Domain of composite of inverse

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    Like a stone-audioslave ADARSH's Avatar
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    Smile [SOLVED] Domain of composite of inverse

    Hi all,

    Q) $\displaystyle Let f :[2,\infty) \rightarrow [1,\infty)$ defined by

    $\displaystyle f(x) = 2 ^{x^4-4x^2} $ and

    $\displaystyle g: [\frac{\pi}{2} , \pi] \rightarrow A $ defined by

    $\displaystyle
    g(x)=\frac{sin(x)+4}{sin(x)-2}
    $

    be two invertible functions , then the what is the domain of $\displaystyle
    f^{-1}(g^{-1}(x))

    $

    my answer is $\displaystyle [ -5, -\frac{(4+sin(1))}{(2-sin(1))}] $
    Is it correct?


    I have got it correctly , checked the answer booklet
    Thanks to all,
    Adarsh
    Last edited by ADARSH; Feb 13th 2009 at 04:13 AM. Reason: Got the answer
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