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+1 vote
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in Sets, Relations and Functions by (395 points)
edited by

If f(x) + 2f (1 – x) = x2 + 2 ∀ x ∈ R, then f(x) =

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1 Answer

+1 vote
by (48.4k points)

f(x) + 2f(1 − x) = x2 + 2   ....(i)

Put x = 1 − x

⇒ f(1 − x) + 2f(x) = (1 − x)2 + 2

Multiply by 2

⇒ 2f(1 − x) + 4f(x) = 2(1 − x)2 + 4  ....(ii)

Subtract (ii) from (i)

−3f(x) = x− 2 −2 (1−x)2

−3f(x) = x2 − 2 − 2x+ 4x

−3f(x) = −(x−4x + 4)

\(f(x) = \frac{(x - 2)^2}{3}\)

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