Finding the Inverse of Cubic Functions

[devious_]

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) = ?

 

[Zurtex]

Yes but it is big and nasty.

In the same way you can have:

$$y = ax^2 + bx + c$$

$$ax^2 + bx + (c - y) = 0$$

$$x = \frac{-b \pm \sqrt{b^2 - 4a(c-y)}}{2a}$$

You can do it for cubic equations with this equation: http://www.math.vanderbilt.edu/~schectex/courses/cubic/

 

[devious_]

Thanks. Just what I was looking for.