求函數f(x)的解析式

2x * f(x) + (x - 3) * f(1/(1-x)) = 4x² - 10x - 1/2 ... (1)
令 y = 1/(1-x) , 則 1/(1-y) = (x-1)/x = z , 那麼 1/(1-z) = x。
分別以y , z 代入(1) 得 :2x * f(x) + (x - 3) * f(y) = 4x² - 10x - 1/2 ... (1)2y * f(y) + (y - 3) * f(z) = 4y² - 10y - 1/2 ... (2)2z * f(z) + (z - 3) * f(x) = 4z² - 10z - 1/2 ... (3)
(1) * 2y - (2) * (x - 3) 得 :
4xy * f(x) - (x - 3)(y - 3) * f(z) = 2y(4x² - 10x - 1/2) - (x - 3)(4y² - 10y - 1/2) ...(4)

(4) * 2z + (3) * (x - 3)(y - 3) 得 :8xyz * f(x) + (x - 3)(y - 3)(z - 3) * f(x)
= yz(16x² - 40x - 2) - z(x - 3)(8y² - 20y - 1) + (x - 3)(y - 3)(4z² - 10z - 1/2)
注意
y = 1/(1-x) , z = (x-1)/x , xyz = - 1 , xy = x/(1-x) , yz = - 1/x , zx = x - 1 。
- 8 * f(x) + (x - 3) (2-3x)/(x-1) (-2x-1)/x * f(x)
= (- 16x + 40 + 2/x) - (x - 1 - 3(x-1)/x)(8/(1-x)² - 20/(1-x) - 1)
+ (x - 3) (2-3x)/(x-1) (4(x-1)²/x² - 10(x-1)/x - 1/2)
(6x³ - 27x² + 9x + 6) / (x(x-1)) * f(x)
= (9x⁴- 93x³ + 180x² - 18x - 48) / (2x²(x - 1))
f(x) = (3x⁴- 31x³ + 60x² - 6x - 16) / (4x⁴- 18x³ + 6x² + 4x)

2012-11-15 20:59:59 補充：
不肯定~我覺得只有這個解~
那個網我看不懂,不過你小心打上連結會被系統扣分~

How come your command is not deleted??
I got few hundred points deleted because of posting links.
Stupid YAHOO server.

☂雨後陽光☀，你咁肯定這條函數方程只有這個解？

不怕好似f(1/x) = xf(x)（http://math.stackexchange.com/questions/28737）咁樣有無限多個解，且任意部分為某種類的函數？