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

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

b. 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.