On inverse permutation polynomials

We give an explicit formula of the inverse polynomial of a permutation polynomial of the form xrf(xs) over a finite field Fq where s|q−1. This generalizes results in [A. Muratović-Ribić, A note on the coefficients of inverse polynomials, Finite Fields Appl. 13 (4) (2007) 977–980] where s=1 or were considered respectively. We also apply our result to several interesting classes of permutation polynomials.