Applications of induced resultants to polynomial maps

Let F(X, Y) be a two dimensional polynomial map over C. We show how to use the notion of induced resultants in order to give short and elementary proofs to the following three theorems: 1. If the Jacobian of F is a non-zero constant, then the image of F contains all of C² except for a finite set. 2. If F is invertible, then the inverse map is determined by the free terms of the induced resultants. 3. If F is invertible, then the degree of F equals the degree of its inverse.