Is there any branch of constructing inverse function exist that is inverse of n functions?

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Is there any branch of constructing inverse function exist that is inverse of   n functions?

ladaroh · Accepted Answer

Let       f    i       (  i  ∈  I  ) be functions with domain       D    i       (  i  ∈  I  ) for a set   I, s.t. the sets       D    i   are pairwise disjoint. Then you can construct a function   f s.t.   f            |                      D        i              =      f    i       (  i  ∈  I  ). If   f is bijective, an inverse function       f          −      1       exists.It then holds that       f          −      1                  |                      f        i            (              D        i            )        =      f    i          −      1      .

Is there any branch of constructing inverse function exist that

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