The question seems too easy to answer, however it is not, since I have to deal with functions that do not have closed forms (or I don't know how to find them). For example, I would like to find inverse functions for: y == x Tan[x] and y == a x + b Tan[x].
Thus far, I used Newton-Rhapson's method for the inverse transformations. It works fine, but requires iterations. I just wonder whether there is a method to prove that there is a better solution or not. I've tried Wolfram Mathematica to find a solution, but since I'm a beginner. I have had no luck to get anything meaningful.
