1. use the inverse function theorem to prove that any function [tex] f: R^2 -> R [/tex] cannot be one-to-one. hint: let(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: One to one functions

**Physics Forums | Science Articles, Homework Help, Discussion**