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) = x2 − 2 −2 (1−x)2
−3f(x) = x2 − 2 − 2x2 + 4x
−3f(x) = −(x2 −4x + 4)
\(f(x) = \frac{(x - 2)^2}{3}\)