Inverse of cubic functions

  1. Is there a way (algebraic or otherwise) to find the inverse function of a cubic polynomial?

    For example:
    y(x) = x³+x-9
    y-1(x) = ?
     
  2. jcsd
  3. Zurtex

    Zurtex 1,123
    Science Advisor
    Homework Helper

    Yes but it is big and nasty.

    In the same way you can have:

    [tex]y = ax^2 + bx + c[/tex]

    [tex]ax^2 + bx + (c - y) = 0[/tex]

    [tex]x = \frac{-b \pm \sqrt{b^2 - 4a(c-y)}}{2a}[/tex]

    You can do it for cubic equations with this equation: http://www.math.vanderbilt.edu/~schectex/courses/cubic/
     
  4. Thanks. Just what I was looking for.
     
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