(Solved): F maps (0,1) -> [0,1]. F(x)={0 if x is irrational and 1/q if x is rational with reduced form p/q, ...

F maps (0,1) -> [0,1]. F(x)={0 if x is irrational and 1/q if x is rational with reduced form p/q, for p & q relatively prime integers. Which of the following is correct: Pick ONE option F is continuous on its full domain F is nowhere continuous F is continuous on the irrationals but not on the rationals F is continuous on the rationals but not on the irrationals