f:[a,b]->R cont., f([a,b]) subset of Q. Prove f constant

[bearej50]

Suppose f : [a, b] ? R is continuous and that f([a, b]) is a subset of Q. Prove that f is constant on [a, b].

 

[stapel]

I think a contradiction proof would probably be the way to go, using the epsilon-delta definition of continuity.