In the previous work: "Explicit construction of inverse functions of polynomials", inverse functions of polynomials were built in an analytical way. 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 got an explicit function FP(y) that satisfies x = FP(P (x)) around x = u.
Now, in this paper, above results are generalized with the aim of building the inverse functions of P(x) around all its roots.
On the other hand, as a potencial application, we are exploring the possibilities of the functions FP(y) in order to find all the roots of polynomial equations and algebraic systems.
