Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If a differentiable function f satisfies f 
= 
∀ x, y ∈ R, then f(x) is equal to
A
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
D
f 
......(1)
differentiate w.r.t. y
f ′ 
replace x with 3x and y with 0
f ′ (x) = –2f ′ (0)
put x = 0 we get f ′ (0) = 0 ⇒ f ′ (x) = 0 ⇒ f(x) = constant
⇒ f(x) = f(0)
in equation (1) put x = 0 = y it gives f(0) = 
⇒ f(x) = 
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