Question

f(x)+2f(1-x)=x^2 +2
then 
f(x)=?

Answer 1

put x=1-x
therefore
f(1-x)+2f(x)=(1-x)^2+2....(2)
multiply by 2
2f(1-x)+4f(x)=2(1-x)^2+4
  (-)
f(x)+2f(1-x)=x^2 +2
-------------------------------
3f(x)=2+x^2-4x+2=x^2-4x+4=(x-2)^2
therefore
$f(x)= \frac{(x-2)^2}{3}$