This paper shows how to build inverse functions of polynomials, from a theoretical point of view. In other words, given a polynomial function y = P (x) = a0 + a1x + ···+amxm, with ai ∈R, 0 ≤ i ≤ m, and a real number, u, so that P′(u) ≠ 0, we get an explicit function FP (y) that satisfies x = FP (P (x)) around x = u. The procedure that we have followed to achieve FP (y) is to compute its Taylor series and its domain of convergence. If u = 0, FP (y) will be denoted by fP (y).
For practical purposes, we are exploring the possibilities of the functions FP (y) in order to solve polynomial equations and algebraic systems.
