find period

edited........

1 Answers

106

Asish Mahapatra ·2010-07-06 18:58:31

f(x+1) + f(x-1) = √2 f(x) .. (1)

so, √2 f(x+1) + √2 f(x-1) = 2 f(x)
=> [f(x+2) + f(x)] + [f(x) + f(x-2)] = 2f(x) [using (1) for f(x+1) and f(x-1)]

=> f(x+2) + f(x-2) = 0 .. (2)

=> f(x-2) + f(x-6) = 0 .. (3)

from (2) and (3),
f(x+2) = f(x-6)
=> f(x) = f(x+8)

so period = 8

calc. errors could be there

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