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**1. Homework Statement**

Prove: If f is defined on the reals and continuous at x=0, and if f(x1+x2)=f(x1)+f(x2) for all x1,x2 in the reals, then f is continuous at all x in the reals.

**2. Homework Equations**

Using defn of limits and continuity

**3. The Attempt at a Solution**

is this like proving that the sum of two functions is continuous? I am a bit confused, this is the last on of the homework, then I can enjoy my easter.