## The Implicit Function Theorem For Functions from Rn to Rn Examples 1 – The Math

Recall from The Implicit Function Theorem for Functions from Rn to Rn page that if $A subseteq mathbb{R}^{n+k}$ is open and $mathbf{f} : A to mathbb{R}^n$ is a continuously differentiable function on $A$ ($mathbf{f}$ is $C^1$ on $A$) then if there exists an $(mathbf{x}_0; mathbf{t}_0) in A$ for which $mathbf{f}(mathbf{x}_0; mathbf{t}_0) = 0$ and the …

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