If f : R → R is a function such that f 5 x + f 5 x + 1 + f 5 x + 2 = 0 , ∀ x ∈ R , then the period of f x is

Question

If f : R → R is a function such that f 5 x + f 5 x + 1 + f 5 x + 2 = 0 , ∀ x ∈ R , then the period of f x is,

MARKS App · Accepted Answer

∵ f 5 x + f 5 x + 1 + f 5 x + 2 = 0 … 1 Replacing x by x + 1 5 in 1 , we get, f 5 x + 1 5 + f 5 x + 1 5 + 1 + f 5 x + 1 5 + 2 = 0 ⇒ f 5 x + 1 + f 5 x + 2 + f 5 x + 3 = 0 … 2 On subtracting 2 from 1 , we get, f 5 x + 3 = f 5 x Now, x → x 5 ⇒ f x + 3 = f x ∴ p e r i o d = 3

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