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Spivak calc problem

  1. Feb 5, 2009 #1
    1. The problem statement, all variables and given/known data

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

    prove f is continuous everywhere


    2. Relevant equations



    3. 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 cant make much headway
     
  2. jcsd
  3. Feb 5, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    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?
     
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