If f(x) + 2f(1- x) = x 2 + 2 ∀ ∀ x ∈ ∈ R, then f(x) is give…

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 11, 2026

If f(x) + 2f(1- x) = x 2 + 2 ∀ ∀ x ∈ ∈ R, then f(x) is given as

x 2 – 2

None of these

Text Solution

Verified by Experts

The correct answer is:

By replacing x with (1 – x) in the given expression, we get

f(1 – x) + 2 f(1- 1 + x) = (1 – x) 2 + 2 ⇒ ⇒ f(1 – x) + 2 f(x)

= (1 - x) 2 + 2

Now f(x) + 2 f(1 – x) – 2(f(1-x) + 2f(x)) = x 2 + 2 – 2

((1 – x) 2 +2)

⇒ ⇒ -3 f(x) = x 2 + 2 – 2(3 – 2x + x 2 )

⇒ ⇒ 3 f(x) = x 2 – 4x + 4 ⇒ ⇒ f(x) =

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