Any function is continuous at point if the following three conditions are satisfied :
1) is defined.
2) exists i.e is finite.
And, of course, there exist both rational and irrational numbers arbitrarily close to any number. So you can take the limit at any number by a sequence of rational numbers or a sequence of irrational numbers. I think you will find that this function is continuous at exactly one value of x. What is that value of x?