If `f(x)`satisfies the relation `f(x)+f(x+4)=f(x+2)+f(x+6)`for all`x , – InterviewSolution

1.	If `f(x)`satisfies the relation `f(x)+f(x+4)=f(x+2)+f(x+6)`for all`x ,`then prove that `f(x)`is periodic and find its period.
Answer» Given `f(x)+f(x+4)=f(x+2)+f(x+6) " (1) " ` Replace x by `x+2`. Then `f(x+2)+f(x+6)=f(x+4)+f(x+8) " (2)" ` From (1) and (2), we have `f(x)=f(x+8).` Hence, `f(x)` is periodic with period 8.

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