What must actually be specified in order for a function to be fully defined / or in what combinations if not all 3 need to be specified? I.e - from knowing the function you can determine the co-domain - e.g - if it is specified that real functions are going in, and for something simple like 2x + 1 = f(x) - then surely from this you can deduce the co-domain will also be all reals. - also say if the co-domain and function have both been specified, then given either the domain/range - surely you are able to deduce domain/range accordingly. - E.g - x^1/2. Am I correct in thinking that its inverse can only be formed if you either: - restrict the domain or - restrict the codomain I am pretty certain the 1st option holds, however for the 2nd is my defintion of co-domain correct? Thanks alot if anyone will shed some light on this, greatly appreciated :).