Invertible Non-Linear Transformation

[tangibleLime]

Homework Statement

Is this invertible? If so, find the inverse.

$$\left( \begin{array}{ccc} y_{1} \\ y_{2} \end{array} \right) = \left( \begin{array}{ccc} x_{1}^{3} \\ x_{2} \end{array} \right)$$

Homework Equations

The Attempt at a Solution

I know that an invertible LINEAR transformation is a L.T. (linear transformation) that can be reversed (right?), so that if L : Rⁿ -> Rⁿ, M : Rⁿ -> Rⁿ, $$M \circ L$$ results in the identity matrix of n.

However, I don't really know how to go about finding this, and besides, it is noted that this is a NON-linear transformation (now I'm really clueless). I also don't know how to prove this is invertible without just showing an inverse as my proof. Any help would be great.

Thanks.

 

[lanedance]

this can be thought of as two separate single variable functions if it helps as
y1=y1(x1) and y2=y2(x2)

also do you know about jacobians and the inverse function theorem?