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