Proving f is Continuous Everywhere: Spivak Calc Problem

[cesc]

Homework Statement

f is a function that satisfies
f(x+y)=f(x)+f(y) and f is continuous at 0.

prove f is continuous everywhere

Homework Equations

The Attempt at a Solution

its easy to see that f(0)=0

My hunch is that the only soln f= cx, and f=0;
but otherwise can't make much headway

 

[Dick]

Write down the definition of continuous at x=0 using f(0)=0. Substitute x-a for x. Can you change it into the definition of f being continuous at x=a?