If $f(x)+2 f(1-x)=x^2+2~ \forall~ x \in R$, then $f(x)$ is given as

$\frac{(x-2)^2}{3}$ $x^2-2$ 1 None of these

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

$f(x)+2f(1-x)=x^2+2$   ....(1) $f(1-x)+2f(x)=(1-x)^2+2$   ....(2) eq. 2 × 2 - eq. 1 $2f(1-x)+4f(x)=2(x^2+1-2x)+4-f(x)+2f(1-x)=x^2+2$ $3f(x)=(x-2)^2$ $f(x)=\frac{(x-2)^2}{3}$