The function f(x)={0,x   is  irrational1,x  is  rational  is

If a is any real number, then every numbered of a contains infinitely many rational as well as infinitely irrational points. ∴f(x)=0  or 1 in every numbered of a.∴Ltx→0f(x)  does not exist∴f(x)  is discontinuous everywhere.