Proving the Implicit Function Theorem From the Inverse Fucntion Theorem.
The homework problem was to prove the Implicit Function Theorem as a Corrollary of of the Inverse Function Theorem for F(x,y) is C(1) on some neighborhood of (a,b) and F(a,b). The book's hint was Use
G(x,y) = (x, F(x,y)) and apply the Inverse FT to that transformation.
I tried running with this hint, even though I had no idea how to use it, the only conclusion I could come to was that on some neighboorhood of (a,0),
the inverse of G maps this neighboorhood on a 1 to 1 map to a neighborhood of the point (a,b).
Its a very classical problem/corrollary and its aggravting that I failed to get it right, so hopefully when I get back from class later today someone will show me what I did wrong.