Let f: R→R have the property that for every u and v in R.
(a) Prove: If f(1)=m, then f(x)=mx for all rational numbers x.
(b) Prove: If f is continuous, then f(x)=mx for all x ∈ R.
The Attempt at a Solution
I am really lost on this problem. We have kind of rushed through the topic of continuity, but I believe I should use the MVT on part (a) and the definition of continuity on part (b).