1. The problem statement, all variables and given/known data I'm trying to do a problem, and in order to do it I need to find a function f:R→R which is continuous on all of R, where A[itex]\subseteq[/itex]R is open but f(A) is not. Can anyone give an example of a function that satisfies these properties? I think once I have an example I'll understand things a lot better. Thanks.