1. The problem statement, all variables and given/known data Let f: R→R have the property that for every u and v in R. f(u+v)=f(u)+f(v) (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. 2. Relevant equations 3. 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).