Prove that the function f defined by if is rational and if x is irrational is continuous at 0 only .

Ok so I was thinking doing it this way:

such that , , and

such that , , and

Then,

So then if I say something like there exists a sequence of rational numbers such that and a sequence of irrational number such that . And then show that there limits are the same would that show that it is only continuous at 0???