Question

“已知2xf(x)+f[1/(1-x)]=2x,求f(x).”的解题思路.

Answer 1

用1/(1-x)代替x代入原式,得到

2/(1-x) f[1/(1-x)[ + f[(x-1)/x] = 2/(1-x)

再用(x-1)/x代入原式,得到

2(x-1)/x f[(x-1)/x] + f(x) = 2(x-1)/x

利用这三个方程可以解出f(x)