33. Given each of the following functions that maps X = {1, 2, 3} to Y = {A, B, C}

f(1) = A, f(2) = B, f(3) = A

g(1) = C, g(2) = B, g(3) = A

Determine whether the function has an inverse. If it has an inverse, provide it. If it does not, explain why not.

34. Refer to the functions in problem 33. What are domain and codomain of both functions? What is the range of each of them?

35. Draw arrow diagrams for both functions defined in problem 33.

5. Given the following two functions f: R R and g: R R are defined by the rules:

f(x) = x2 + 10x + 7

g(y) = 5y + 9

Find f g and g f.