Question

Find the period of the given functional statement: f(x+1)+f(x-1)=√2f(x)​

Answer 1

Make x=x+1

f(x+2)+f(x)=√2

f(x+1)

Now sum (1) and (2):

2f(x)+f(x+2)+f(x−2)=√2

(f(x+1)+f(x−1))=2f(x)

f(x+2)+f(x−2)=0

Now make x=x+2 then f(x+4)=−f(x).

Make x+4 and get f(x+8)=−f(+4)=f(x), then the period is 8.

Answer 2

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