Piecewise constructions of inverses of some permutation polynomials

It is a hard problem to find the inverse of a nontrivial class of permutation polynomials of finite fields. In this paper the piecewise method is employed to construct the inverses of permutation polynomials, although piecewise constructing permutation polynomials is not a new idea. A formula for the inverses of some permutation polynomials of finite fields is presented.