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

$f(x)+2f(1-x)=x^2+2$ …(i)

Replacing x by 1 – x in (i), we get ⇒ $f(1-x)+2f(x)=(1-x)^2+2$

$⇒ f(1-x)+2f(x)=x^2-2x+3$ …(ii)

Eliminating f(1− x) from (i) and (ii), $f(x)=\frac{(x-2)^2}{3}$