Question 1. Let K be an algebraically closed field. (1) Consider the polynomial map F : K2 - K, (X, Y) > Y. Show that the image F(V) of the affine variety V = V(XY - 1) is open. (2) Let F : K" -> Km be a polynomial map, and let W = V(91, 92, . . . ,gk) C Km be an affine variety. Show that the inverse image F-'(W ) of W is V (g1 0 F, 92 0 F, . .., gk . F), thus is an affine variety