Prove or give a counterexample. let $f \colon R \to R$ such that $f$ is continuous on $D \subseteq R$ and $f$ is continuous on $S \subseteq R$. Then f is continuous on $D \cup S$. I am kind of puzzled with notation ($f$ is continuous on $D \subseteq R$ and $f$ is continuous on $S \subseteq R$. Then $f$ is continuous on $D \cup S$) Can you give me an example?
What if I consider this example: f(x) = x if x is rational and f(x) = 0 if x is irrational. Then I will have that f is continuous only at 0.( a counterexample)?