Find the period of real valued function satisfying
f(x) +. f(x+4). =f(x+2) + f(x+6)

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Solution

f(x)+f(x+4)=f(x+2)+f(x+6) ...1
lets replace x by x+2
f(x+2)+f(x+6)=f(x+4)+f(x+8) ...2
from equations 1 and 2 we get
f(x)+f(x+4)=f(x+4)+f(x+8)
or f(x)=f(x+8)
So, the period is 8

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f (x) + f (x + 4) = f (x + 2) + f (x + 6)

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\int_{x}^{x + 8} f (z) d z

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