find the period

Let f(x) be a function defined as f(x-1)+f(x+1)=f(x)
then what iz the period of the function f(x)?
(1)8
(2)4
(3)2
(4)12
answer me with explanation

4 Answers

r u sure of teh options ....im getting period as 6

yes...........i m too getting 6

but the answer is given 8.can u sayme how u found 6

array bhai...

firstly replace x by x+1 in original eq

f(x)+f(x+2)=f(x+1)..............2

f(x-1)+f(x+1)=f(x).............1

add eq 1 and 2

f(x+2)+f(x-1)=0.......3

replacing x by x+1 in eq 3

f(x+3)+f(x)=0

f(x+3)=-f(x)........................4

Now replace x by x-1 in original eq and then add similarly with original eq and replacing x by x-1 we get f(x-3)+f(x)=0..........5

from eq 4 and 5 we get f(x-3)=f(x+3)
replacing x by x-3

we get f(x)=f(x-6)

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