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Inverse functions for f:R^m-->R^m , or f:X^m-->Y^m
Hi:
This is , I guess a technical question:
Given f:R^m --->R^m ; f=(f_1(x_1,..,x_m),...,f_m(x_1,...,x_m))
Then I guess f^-1 (of course, assume f is 1-1.). Is given by a "pointwise" inverse ,
(right?) i.e.,
f^-1 =(f_1^-1 (x_1,..,x_m) ,...,f_m^-1(x_1,..,x_m)) ?.
Is there some theorem on existence of inverses if we only know f to be
continuous ( I think there is no known test for whether a function into R^m
is onto )?
Thanks.
Hi:
This is , I guess a technical question:
Given f:R^m --->R^m ; f=(f_1(x_1,..,x_m),...,f_m(x_1,...,x_m))
Then I guess f^-1 (of course, assume f is 1-1.). Is given by a "pointwise" inverse ,
(right?) i.e.,
f^-1 =(f_1^-1 (x_1,..,x_m) ,...,f_m^-1(x_1,..,x_m)) ?.
Is there some theorem on existence of inverses if we only know f to be
continuous ( I think there is no known test for whether a function into R^m
is onto )?
Thanks.