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) = ?
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/