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CGP EDU Academic Team
Published on: August 12, 2026
'f ' is a real valued function not identically zero, satisfying f(x + y) + f(x - y) = 2f(x). f(y) ∀ ∀ x, y ∈ ∈ R. f(x) is definitely
Text Solution
Verified by ExpertsThe correct answer is:
B
Putting x = 0, y = 0 in the functional equation we get 2f(0) = 2f 2 (0) ⇒ ⇒ f(0) = 0, 1. But if f(0) is equal to zero then f(x) = 0 ∀ ∀ x ∈ ∈ R. Thus f(0) = 1. Now putting x = 0 in the functional equation we get, f(y) + f(-y) = 2f(0). f(y)
⇒ ⇒ f(y) = f(-y). Thus f(x) is even.
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