The fundamental theorem on functional identities states that a prime ring R with deg ( R ) ≥ d is a d -free subset of its maximal left ring of quotients Q m l ( R ). We consider the question whether the same conclusion holds for symmetric rings of quotients. This indeed turns out to be the case for the maximal symmetric ring of quotients Q m s ( R ), but not for the symmetric Martindale ring of quotients Q s ( R ). We show, however, that if the maps from the basic functional identities have their ranges in R , then the maps from their standard solutions have their ranges in Q s ( R ). We actually prove a more general theorem which implies both aforementioned results. Its proof is somewhat shorter and more compact than the standard proof used for establishing d -freeness in various situations.