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Math Help - functions

  1. #1
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    functions

    Let f(x) the function defined below, where -1 < x < 1.



    a) Find f -1(7).

    (b) Find f(f -1(8)).


    I'm having a tough time finding the inverse.
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  2. #2
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    Quote Originally Posted by leftyguitarjoe View Post
    Let f(x) the function defined below, where -1 < x < 1.



    a) Find f -1(7).
    Find x such that :
    7=7+x^2+\tan\left(\frac{\pi x}{2}\right)

    One advice : x^2 \ge 0 and since -1<x<1, -\frac \pi 2 < \underbrace{\frac{\pi x}{2}}_{t} < \frac \pi 2

    One knows that from -\frac \pi 2 and \frac \pi 2, tan(t) is strictly increasing (from - infinity to + infinity). So it has only one solution if you want to solve tan(t)=...

    Try for x=0.

    (b) Find f(f -1(8)).
    Huh ? Isn't f(f^{-1}(x))=x ? (if f is a bijection ^-^)

    I'm having a tough time finding the inverse.
    And it will be very hard to find it
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