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

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    it follows from Implicit function theorem? Or is there anything else you have in mind?2012-11-08

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