If f is a function of real variable x satisfying `f(x+4)-f(x+2)+f(x)=0` , then f is periodic function with period:

Options

A. 6
B. 8
C. 10
D. 12

Answer

D

Explanation

We have , f(x+4)-f(x+2)+f(x)=0 for all x .
Replacing x by x +2, we get
f(x+6)-f(x+4)+f(x+2)=0 for all x
Adding (i) and (ii) ,we get
f(x+6)+f(x)=0`" "` …….(iii)
Replacing x by x+6 , we get
f(x+12)+f(x+6)=0`" "`....(iv)
From (iii) and (iv), we obtain
f(x+12)=f(x) for all x
Hence , f(x) is periodic with period 12.