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 $x = F'(u)$