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Even or odd functions

  1. Jun 15, 2013 #1
    1. The problem statement, all variables and given/known data

    1) f(x+1)=f(x)+1
    2) f(x^2) =(f(x))^2
    let a function real to real satisfy the above statements then prove whether the fuction is odd or even.

    2. Relevant equations



    3. The attempt at a solution
    using the 2) we get 1) f(0) = 0,1
    2) f(1) = 0,1
    putting x = 0 in the 1st equation we get f(0) = 0 and f(1) = 1. from this we can prove f(-1) = -1 and for integers we get f(-x) = -f(x). But how to prove for real
     
  2. jcsd
  3. Jun 15, 2013 #2

    mfb

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    Please do not post threads in multiple forums.

    Did you consider ##f(\sqrt{n}^2)## for integers n?
    What about f(1/2) and f(-1/2)?

    I am not sure if it is possible to construct the whole function in that way. Based on your function values, it is trivial to show that the function cannot be even, but that is not sufficient to show that it is odd. Continuity would be nice to have.
     
  4. Jun 15, 2013 #3
    We can say it is not an even function ..then how to prove that it is an odd function.
     
  5. Jun 15, 2013 #4

    haruspex

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    What can you say about |f(x)| compared with|f(-x)| on the one hand, and f(|x|) compared with f(-|x|) on the other?
     
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