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quasar987

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## Main Question or Discussion Point

In the implicit function theorem, we take a C^1 function F:R^n x R^m --> R^m and given a condition on the partial derivatives at a point (x_0,y_0) such that F(x_0,y_0)=0, we conclude that the relation F(x,y)=0 implicitely defines a function f(x)=y in a nbh of x_0. I.e. the last m variables are determined by the first n in a nbh of x_0.

What if I want to express the last k variable (where k differs from m) in terms of the others?

Is this impossible?

What if I want to express the last k variable (where k differs from m) in terms of the others?

Is this impossible?