Let a = {a, b, c, d, e} and b = {2, 4, 6, 8, 10, 12, 14}. (a) define the map f whose domain is a and whose output is b by f(a) = 8, f(b) = 2, f(c) = 14, f(d) = 12, f(e) = 6. write down a function g whose domain is b and output is in a such that (g ◦ f)(x) = x for all x ∈ a.