Consider the functions f: AB, g: BC, and h: CD, where A = {b}, B = {a, b, z}, C = {}, and D = {1, 2, 3}. The functions are defined by the following relations: f = {(b, b)}, g = {(a, a), (y, y), (z, z)}, h = {(2, 2), (3, 3)}.
(a) Define f^(-1) or explain why it is not invertible.
(b) Define h o g (as a set of ordered pairs).
(c) Define g o f (as a set of ordered pairs).
(d) Are h o g o f and h o g o f the same function? Why or why not?