Define F: R R R R as follows: F(x, y) = (3y 1, 1 x) for all (x, y) in R R. (a) F(0, 0) = ? F(1, 4) = ? (b) Is F one-to-one? Prove or give a counterexample. (c) Is F onto? Prove or give a counterexample. (d) Is F a one-to-one correspondence? If not, explain why not. If yes, find F 1 .