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If a function satisfies f(x+1)+f(x-1)=root(2).f(x),...

  1. Aug 9, 2015 #1

    Titan97

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    1. The problem statement, all variables and given/known data
    If a function satisfies f(x+1)+f(x-1)=√2.f(x), the the period of f(x)=_____

    2. Relevant equations
    none

    3. The attempt at a solution
    I first tried to get rid of the irrational term.
    f(x+2)+f(x)= √2.f(x+1)
    f(x)+f(x-2) = √2.f(x-1)

    adding the above equation, and substituting the given equation,

    f(x+2)+f(x-2)+2f(x)=√2.(√2.f(x))=2f(x)
    f(x+2)+f(x-2)=0
    f(x+4)+f(x)=0

    Now instead of getting f(a-x)=f(x) equation, i am getting f(a-x)=-f(x). How can I find its period?
     
  2. jcsd
  3. Aug 9, 2015 #2

    Orodruin

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    If f(x+a) = -f(x), what is f(x+2a)?
     
  4. Aug 9, 2015 #3

    Titan97

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    f(x+2a)=f((x+a)+a)=-f(x+a)=f(x):headbang: I did not think it was this easy.
     
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