若f(x)满足2f(x)+x2f(1/x)=(3x3+x2+4x+3)/(x+1)，求f(x)．
【正确答案】：令u=1/x，则x=1/u． 2f(x)+x2f(1/x)=(3x3+x2+4x+3)/(x+1) (1) 变为 2f(1/u)+1/u2f(u)=(3/u3-1/u2+4/u+3)/(1/u+1)=(3/u3-1/u+4+3u)/(u+1) 即 2f(1/x)+1/x2f(x)=(3/x2-1/x+4+3x)/(x+1) (2) (1)×2-(2)×x2 解得 f(x)=(x3-2x3+3x+1)/(x+1)
