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Dear Vivek
f(x)+f(x+4)=f(x+2)+f(x+6) ........(1)
Replacing x by x+2, we get
f(x+2)+f(x+6)=f(x+4)+f(x+8) .......(2)
from (1) and (2)
f(x)+f(x+4)=f(x+4)+f(x+8)
==>f(x)=f(x+8)
==>Period =8
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