21r u sure of teh options ....im getting period as 6
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
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UP 0 DOWN 0 0 4
4 Answers
21array 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)