Question

For what values of x is the function f de-
fined by
f(x) = 1 , x rational
2 , x irrational ,
continuous?
1. only at rational x
2. only at x = 0
3. all x
4. only at irrational x
5. no x

Answer 1

nowhere

Answer 2

no matter what small interval you take there will be rational and irrational numbers contained in it, so the function will be both 1 and 2 in any interval. therefore it is continuous nowhere