[Oriel]

$$f(2011x-f(0))=2011x^2$$
$$f(x)=2011\left(\frac{x+f(0)}{2011}\right)^2$$
แทนค่า $x=0$
$$f(0)=2011\left(\frac{0+f(0)}{2011}\right)^2=\frac{f(0)^2}{2011}$$
$$f(0)^2-2011f(0)=f(0)(f(0)-2011)=0$$
$$\therefore f(0)=0,2011$$
หา$f(2011)$
ได้ $2011,8044$