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Titan97
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Homework Statement
If a function satisfies f(x+1)+f(x-1)=√2.f(x), the the period of f(x)=_____
Homework Equations
none
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?