Math Help - Commutativity of Inverse Functions.

Let, be a real valued function definited for all reals. Proof (or disproof) that is there exists a function such as is true for all reals. Then, is always true.

Originally Posted by ThePerfectHacker

Let, be a real valued function definited for all reals. Proof (or disproof) that is there exists a function such as is true for all reals. Then, is always true.

Let be a sigmoid function something like the cumulative
normal functiom, then is mapped one one onto
, and so there is an inverse function from
onto

Then holds for all but not for all

That is the domains of and are not equal.

RonL