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## Homework Statement

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.

## Homework Equations

## 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).