On a family of preimage-resistant functions

In the present paper we define a new hash function, based on inhomogeneous polynomials. First we define a large family of polynomials over finite fields and we prove that the members of this family are nearly permutational polynomials. Then we define a subfamily of the above family, such that the elements in the subfamily are easy to evaluate. We prove that (working in a large enough finite field) finding a preimage by chance of such a function is computationally infeasible, and we mention that methods for solving the equation corresponding to the preimage problem for such polynomials are also out of reach.