To find the inverse function . If then replace the and so , now find an expression in function of . So you will get the inverse function.
Sorry, I just wanted to give a 'general' solution to calculate the inverse function, but indeed in this case that would be really hard because of the third degree, if you have a first degree or second degree function it's less complicated.
In this case it's not very hard. We have the equation i.e. . Then, which implies the equation has only one real root. So, using the well known formula for the roots:
We can inmediately verify that the product of the two real cubic roots of the above addends is . So, we can express
where we choose for each addend the real cubic root.