Let E = {(x, y): 0 < y < x} and set f(x, y) = (x + y, xy) for (x, y) ∈ E.
a) Prove that f is 1-1 from E onto {(s, t): s > 2√t, t > 0} and find a formula for f-1[ (s, t).
b) Use the Inverse Function Theorem to compute D(f-1)(f(x, y)) for U, y) ∈ E.
c) Use the formula you obtained in part a) to compute D(f-l)(s, t) directly. Check to see that this answer agrees with the one you found in part b).