Let $\displaystyle f: \mathbb{R}^{k+n} \rightarrow \mathbb{R}^n $ be of class $\displaystyle C^1 $; suppose that f(a) = 0 and that Df(a) has rank n. Show that if c is a point of $\displaystyle \mathbb{R}^n $ sufficiently close to 0, then the equation f(x) = c has a solution.

I'm pretty sure that I have to use the implicit function theorem here, but I'm not sure how to proceed. Any ideas?