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Supplementary question to interesting problem post

  1. Mar 8, 2013 #1

    jdp

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    Supplementary question to "interesting problem" post

    If f(2x)=f(f(x))
    and f(2x+1)=f(2x)+1

    then for what value n such that n is in the set of natural numbers could f(0) equal 2^n.

    also for what value n does f(0) equal 2^n +2?
     
  2. jcsd
  3. Mar 9, 2013 #2

    Bacle2

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    Science Advisor

    Why don't you get some data by working with simple values for x, like 1,0, etc?

    You get : f(0)=f(f(0))
    f(1)=f(0)+1

    Use x=-1/2 , then f(-1)=f(f(-1/2)
    f(0)=f(-1)+1

    for x=-1 , f(-1)=f(-2)+1 ......
     
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