# How is the inverse of $y=4x^3 - 3x^4$ found?

I would like to calculate the inverse of $$y = 4x^3 - 3x^4$$ on the domain $$x = [0,1]$$.

What would be the best way to tackle this?

I'd preferably a general method, suitable for tackling other nontrivial functions.

If it is not possible to have an explicit/exact solution for this, how else would you get a drawing from a particular pdf via Matlab/Java/Python?

My idea was to use the inverse transformation method for the cdf and then use the uniform distribution with $$x = F'(u)$$