Let S = {1, 2, 3, 4, 5} and T = {1, 2, 3, 8, 9} and define functions f: S->T and g: S ->S by f = {(1, 8), (3, 9), (4, 3), (2, 1), (5, 2)} and g = {(1, 2), (3, 1), (2, 2), (4, 3), (5, 2)}.

i. Find f g or explain or explain why f g is not defined.

ii. Which of f, g are one-to-one? Which are onto? Explain why.

iii. Find f-1 if it exists. If it doesn't, explain why not.

iv. Find g-1 if it exists. If it doesn't, explain why not.