If 2 f xy = f x y + f y x for all x, y ∈ R and f 1 = 3 , then the value of Σ r = 1 1 0 f r is equal to

Question

If 2 f xy = f x y + f y x for all x, y ∈ R and f 1 = 3 , then the value of Σ r = 1 1 0 f r is equal to, 3 2 3 1 0 - 1, 3 2 3 9 - 1, 3 1 0 - 1 2, 1 2 3 1 0 - 1

MARKS App · Accepted Answer

From given functional equation, 2 f xy = f x y + f y x , ∀ x, y ∈ R putting y = 1 , 2 f x = f x + f 1 x f x = 3 x ∴ Σ r = 1 1 0 f r = Σ r = 1 1 0 3 r = 3 3 1 0 - 1 3 - 1 = 3 2 3 1 0 - 1

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