Let A = R × R and f : A → A be given by the rule f(x, y) = (x − y, x + y). (a) Prove f is one-to-one. (b) Prove f is onto A. (Comment: don’t forget that if given b ∈ A, you construct a such that f(a) = b, you must also show a ∈ A.) (c) What is the inverse function? (d) Is f a permutation? Explain