f(x)=1/x , g(x)=x , a=0
i think "a" should remain as itself, and that way your answer converts to this.
f(x)=1/(x-a) and g(x)=(x-a)
when you appy this to f(x)-g(x);
i couldn't understand how it's converges.
btw, my head is really full today, cuz of exams. so if it's answer is too easy sorry for bothering.
edit: and sorry again for my bad grammer. =)
Again, not defined for irrational x and so the limit would not exist.And
f(x)-g(x) for rational.
There are no such f and g for the reason snowtea cited.