XPost: sci.math   
   From: ivgroups@onlinehome.de   
      
   "Dale"  wrote in news:lvkue5$vu9$1@speranza.aioe.org...   
   >>>> I am interested here in *symbolically* given functions, that means in   
   >>>> expressions of some Special functions (Named functions) (Wikipedia:   
   >>>> Special functions), e.g. the Elementary functions (Wikipedia:   
   >>>> Elementary   
   >>>> function).   
   >>>> try just (since it is a function);   
   >>>> y = f(x)   
      
   >>>> When (under what conditions) is the inverse of a symbolically given   
   >>>> function also a function which can be represented symbolically?   
   >>> f−1(f(x)) = x = f(f−1(x))   (the f is followed by superscripted -1   
   >>> meaning inverse, not exponentation)   
   >>> thar you go. all done.   
      
   >> You are right. Each inverse function can be represented symbolically if   
   >> we name the inverse. But is it possible to name all ever imaginable   
   >> functions? Please consider, I am interested in the *general*   
   >> mathematical problem, not only in the problem for only one given   
   >> function! Therefore my hint to Liouville's theorem!   
      
   > it is general functional form, symbolic.   
   > applies to any function.   
   > Cant get any simpler,   
   > except it dosent have to be a "function", but could be multi valued.   
      
   I do not at all know what you want from me! I above defined what we mean in   
   this thread by "symbolically" (or "symbolic"). You can replace   
   "symbolically" by "in closed forms" or by "in finite terms".   
   At least partial solutions of the general problem could be possible. Take   
   e.g. expressions of some Elementary Special functions, the Elementary   
   functions, or expressions of some Non-elementary Special functions, or   
   expressions of the or some Elementary functions and some Non-elementary   
   Special functions. You can take the Liouvillian functions or the algebra   
   used in the ansatz for Liouville's theorem as an example.   
      
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