Ahomomorphism is a function f : σ−→γ∗ from one alphabet to strings over another alphabet. we can extend f to operate on strings by defining f(w) = f(w1)f(w2)··· f(wn), where w = w1w2 ··· win and each wi ∈ σ. we further extend f to operate on languages by defining f(a) = {f(w)| w ∈ a}, for any language a. a. show, by giving a formal construction, that the class of regular languages is closed under homomorphism. in other words, given a dfa m that recognizes b and a homomorphism f, construct a finite automaton m′ that recognizes f(b). consider the machine m′ that you constructed. is it a dfa in every case?