So here's the problem: Let n > m, Suppose that f: R_n to R_m is continuously differentiable, and suppose df at 0 is onto. Show that there is a positive constant r such that f(R_n) contains the whole ball of radius r around f(0).

I'm not exactly sure how knowing df at 0 is onto is helpful to this problem, and I'm not even sure how to begin to tackle this proof, so any help would be appreciated!