Prove f(y) = y for every real number y

[Annie B]

A function f: R->R is a continuous function such that f(q) = q for every rational number q.
Prove f(y) = y for every real number y.

I know every irrational number is the limit to a sequence of rational numbers. But I not sure how to prove f(y) = y for every real number y. Any ideas?

 

[mfb]

I moved your thread to our homework forums.

You can use exactly that property about limits, together with continuity.