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. =)
What is g for x irrational? If you mean that g is not defined for x irrational then does not exist. In order that exist, you would have to have g(x)= 1 for x irrational also (at least close to a) and in that case, would not exist.
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.