1. use the inverse function theorem to prove that any function [tex] f: R^2 -> R [/tex] cannot be one-to-one. hint: let g(x,y) = (f(x,y), y) near an appropriate point. 2. prove #1 using the implicit function theorem. 3. generalize part 2) to show that no function [tex] f:R^n -> R^m, [/tex] with n>m can be one-to-one. i am not sure where to start on this problem. for #1, i don't know how to apply the hint that's given. what is this "appropriate point" it's referring to? i guess i started by trying to take the determinant of f'(x,y). but f'(x,y) is a 2x1 matrix...how do i take determinant of that? not sure where this is leading me. not sure what to do for #2 or #3 either. my understanding of the implicit function theorem is very fuzzy. like, i understand how to use it to differentiate one variable with respect to another, but i don't know how to use it to prove the function is not one to one. any help is appreciated - thanks in advance.