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

$f(x)+2f(1-x)=x^2+2$   ....(1)

$f(1-x)+2f(x)=(1-x)^2+2$   ....(2)

eq. 2 × 2 - eq. 1

$2f(1-x)+4f(x)=2(x^2+1-2x)+4-f(x)+2f(1-x)=x^2+2$

$3f(x)=(x-2)^2$

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