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I have read by the advice of Mr.mixed math,and Mr.willie wong that inverse of a multi variable function can be found out using the theorem present here ,so in that case the author mentions about taking the function $b=f(a)$ ,where that becomes generally a function of single variable ,

I was looking for the advanced version of Inverse function Theorem that accounts for multivariate type, i mean how can the same theorem used to find the inverse of a multivariable function,even though it is profound that many-to-one functions are not invertible,but one can talk about the correspondence ,and someway find the inverse,

so did anybody read anything related to that???, thanking you a lot, for patiently answering my questions

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Read a few more words, please! In the very same Wikipedia article you linked to, there is a section called Generalisations, where it is mentioned that the domain can even be allowed to be infinite dimensional manifolds. – Willie Wong Sep 4 '11 at 11:52
@Willie Wong:yes sir ,but they didnt mention the precise way of doing it,so i created a separate question,anyway thanks a lot sir – Iyengar Sep 4 '11 at 14:49
@Willie I blame your two-word name for my transformation into Mr. Mixed Math – mixedmath Sep 4 '11 at 16:17
up vote 1 down vote accepted

Those are the level sets if I am understanding your question correctly. In that case: the gradient of a function is perpendicular to the level curve at every point.

Let's say we have the following situation: $z=f(a,b)$

Then the implicit curve defined by this equation is perpendicular to $\nabla f(a,b)$

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