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We investigate the permutation property of polynomials of the form$x^{r}(x^{s} -a)^{t}$, and give the expressions of their inverses. Inparticular, explicit expressions of inverses of permutation polynomials $x(x^3-a)^2$ and $x(x^2 -a)^3$ on $\mathbb{F}_{7^n}$ are presented. Then, using someknown results, we obtain the inverses of all permutation polynomials of degree$6, 7, 8$ over finite fields.

On inverse of permutation polynomials of small degree over finite fields, II