设f(x)=1nx且函数φ(x)的反函数φ^-1(x)=(x-1)/(x+2)，则φ[f(x)]

设f(x)=1nx且函数φ(x)的反函数φ^-1(x)=(x-1)/(x+2)，则φ[f(x)]

(2lnx+1)/(1-lnx) 分析：由y=φ^-1(x)=(x-1)+(x+2)得yx+2y=x-1，x=(2y+1)/(1-y)，故φ(x)=(2x+1)/(1-x)，所以φ[f(x)]=(2lnx+1)/(1-lnx)．