Finding the period of f(x+1)+f(x-1)=√2·f(x)

[Titan97]

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?

 

[Orodruin]

If f(x+a) = -f(x), what is f(x+2a)?

 

[Titan97]

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