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Math Help - Showing one to one

  1. #1
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    Showing one to one

    f(x) = 2x^3 - (cosx)^3, x for all [0, pi]. Show f is one to one and find (f^-1)'(-1). Note (0,-1) for all f.

    x = 2y^3 - (cosy)^3

    Is there a way I can factor the y so there is only one of them?
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  2. #2
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    On \left( {0,\pi } \right) observe that f'(x) \ge 0. That means that f is increasing there.
    Moreover, f(0) =  - 1.
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