Help with functions?

Question

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

What is f(x)?

Answer 1

3f(x) +f(2-x) =x^2
3f(2-x) +f(0) = (2-x)^2
multiplying the first by 3 and subtracting
9f(x) -f(0) = 3x^2-(2-x)^2
To calculate f(0)
3f(0) +f(2) = 0 and
3f(2)+f(0) =4
so f(2)=-3f(0)
-9f(0)+ f(0) =4 so f(0) = -1/2
so f(x) = 1/9[3x^2-(2-x)^2-1/2]

Answer 2

♦ suppose it is y(x)=ax^2+bx+c;
then 3(ax^2+bx+c) +a(2-x)^2+b(2-x)+c =x^2;
3ax^2 +3bx +3c +4a –4ax +ax^2 +2b –bx +c = x^2,
♠ thence 4a =1, 2b -4a = 0, 4c+4a+2b=0;
♥ hence a=0.25, b=0.5, c=-0.5; thus
y(x) = 0.25x^2 +0.5x –0.5;