Algorithmics course, please explain thoroughly, I'm trying to understand.

2. (standard, 20pt) Let be an alphabet. For a word w=a1an and a (total) function h from to , we use h(w) to denote h(a1)h(an). For a language L over the alphabet, we use h(L) to denote {h(w):wL}. Prove that (1). If L is a regular language, then so is h(L). (2). There is a non-regular language L such that h(L) is a regular language for some h