6. Let E = {(x, y) : 0 < y < x} and set f (x, y) = (x + y, xy) for (x, y) E E.

(a) Prove that f is 1-1 from E onto {(s, t) : s > 20, t > O} and find a formula for f-1(S,t).

(b) Use the Inverse Function Theorem to compute D(f-1 )(f(x, y)) for (x, y) E E.

(c) Use the formula you obtained in part

(a) to compute D(f-1)(S,t) directly.

Check to see that this answer agrees with the one you found in part (b).