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Math Help - Inverse function question

  1. #1
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    Inverse function question

    Suppose f(x) coincides with its inverse over a suitable interval.


    Suppose that f(x) = \frac{ax+b}{cx+d}. What conditions on a,b,c,d are necessary and sufficient in order that f(x) coincide with it's inverse function?

    Help is greatly appreciated. Thanks.
    Last edited by Iceflash234; April 10th 2010 at 12:33 PM. Reason: typo
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  2. #2
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    f^{-1}(x) = {b-dx\over cx-a}

    btw, I think you meant ax+b\over cx + \color{red}d.
    Last edited by maddas; April 10th 2010 at 12:43 PM. Reason: typo lol
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  3. #3
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    Quote Originally Posted by maddas View Post
    f^{-1}(x) = {b-dx\over cy-a}

    btw, I think you meant ax+b\over cx + \color{red}d.
    Thanks. Fixed the typo.

    About response: Ok. I understand that. But what conditions on a,b,c,d are are necessary and sufficient?
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  4. #4
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    lol that y was supposed to be an x, sorry!

    Equate f(x) = f^{-1}(x) and clear the denominators. You will arrive at two polynomials in x. Equating their coefficients should give you the required conditions.
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