Last week a few friends and I discussed this "function":

f(x)=ln(1-x)+ln(x-2)

It was seen in a classroom, to which the instructor had written, "the domain is empty, therefore this is NOT a function". On further thinking, though, it does not violate any of the parts of the definition of a function. Sooooo, what would you call it? I have my own idea(s).

p.s. Stay out of the complex's. :)