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Give an example of a function f(x) that is discontinuous at each point of its domain

  1. Oct 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Give an example of a function f(x) that is discontinuous at each point of its domain, whereas f(f(x)) is continuous everywhere.

    2. Relevant equations



    3. The attempt at a solution

    I guess the function has to be defined piecewise, but I don't know how to approach this at all. I'm thinking of making conditions for x rational, x irrational, but I wouldn't know how to make the function discontinuous at ALL irrational points. Maybe the function doesn't need to take on values at all x? I really don't know.
     
  2. jcsd
  3. Oct 25, 2009 #2
    Re: Give an example of a function f(x) that is discontinuous at each point of its dom

    never mind, i figured it out
     
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