1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook