Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If f(x) + 2f(1 - x) = x 2 +1 ∀ ∀ x ∈ ∈ R then f(x) is
A
(x 2 + 4x - 3)
B
(x 2 + 4x – 3)
C
(x 2 – 4x + 3)
D
(x 2 – 4x + 3)
Text Solution
Verified by ExpertsThe correct answer is:
C
f(x) + 2f(1 - x) = x 2 + 1
Replacing x → → (1 - x) we get; f(1 – x) + 2f(x) = (1 -x) 2 + 1
⇒ ⇒ f(1 - x) + 2f(x) = 2 + x 2 - 2x
From these equations we get f(x) = 
(x 2 - 4x + 3)
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