The domain of the function where the rule applies is words that refer to physical locations, such as cities, countries, and landmarks. However, the function does not work correctly for words that do not refer to physical locations, such as "Fidelio" and "The Barber of Seville", which return "undefined". Therefore, the part of the domain where the rule does not hold is words that do not refer to physical locations.

Please let me know if this description accurately reflects the behavior of the function f(x).