f(x) is a function defined from Set of rational numbers Q to itself as
f(x)=x,
Is this function continuous at all rational numbers?
It's continous from $\displaystyle \mathbB R $ to itself (just use $\displaystyle \epsilon = \delta$ in the definition of continuity), hence also continuous when restricted to any subset. So the answer is "yes, it's continuous".Originally Posted by vms
On the other hand, in response to Ene Dene's post, if f(x) is defined as constant c for all real $\displaystyle x \notin \mathbB Q$, then f is continuous at x=c only .