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Math Help - Inverse of rational function

  1. #1
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    Inverse of rational function

    How to prove or disprove the inverse x=f^{-1}(y) of the rational function y=f(x) is also a rational function?
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  2. #2
    MHF Contributor chisigma's Avatar
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    A simple example: y(x)= x^{3} + x is rational but the inverse x(y) is irrational. To prove that is sufficient to consider that the real solution of the equation x^{3} + x -y =0 is obtained using the Cardano's formula, where square and cubic roots are involved...

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    \chi \sigma
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