115 鳳山高中
版主: thepiano
Re: 115 鳳山高中
填充第 6 題
f(x) + 2f((x - 3)/(x + 1)) = x
x 用 (x - 3)/((x + 1) 代入，可得 f((x - 3)/(x + 1)) + 2f((- x - 3)/(x - 1)) = (x - 3)/(x + 1)
x 用 (- x - 3)/((x - 1) 代入，可得 f((- x - 3)/(x - 1)) + 2f(x) = (- x - 3)/(x - 1)
三個式子解聯立，可求出 f(x) = (x^3 - 6x^2 - 9x - 18)/(9x^2 - 9)
f(x) + 2f((x - 3)/(x + 1)) = x
x 用 (x - 3)/((x + 1) 代入，可得 f((x - 3)/(x + 1)) + 2f((- x - 3)/(x - 1)) = (x - 3)/(x + 1)
x 用 (- x - 3)/((x - 1) 代入，可得 f((- x - 3)/(x - 1)) + 2f(x) = (- x - 3)/(x - 1)
三個式子解聯立，可求出 f(x) = (x^3 - 6x^2 - 9x - 18)/(9x^2 - 9)