I'm doing Real Analysis and I'm at a point where I'm exploring continuous functions.
I stumbled on this question
Let A ⊆ R and f : R → R a continuous function such that f(x) = 6 for all x ∈ A. What property must the set A have in order to conclude from this that f(x) = 6 for all x ∈ R? Be sure to give reasons for your answer.
I tried looking for the property but couldn't find anything concrete.
I would really appreciate any help.