设f(x)=(x-1)分之(x+1),则y等于f(x分之1)的反函数是什么
问题描述：
设f(x)=(x-1)分之(x+1),则y等于f(x分之1)的反函数是什么
答
令 y = f(x)，则有：y = (x + 1)/(x - 1) = 1 + 2/(x - 1)
2/(x - 1) = y - 1
x - 1 = 2/(y - 1)
x = 1 + 2/(y - 1)
即 f^(-1)(x) = 1 + 2/(x - 1)
答
f(1/x)=(1/x+1)/(1/x-1)=(1+x)/(1-x)
∴y=(1+x)/(1-x)
y-xy=1+x
y-1=x(y+1)
∴x=(y-1)/(y+1)
即y=(x-1)/(x+1)
答
以下是详细的运算步骤.已知f(x)=(x+1)/(x-1)所以y=f(1/x)=(1/x+1)/(1/x-1)=[(1+x)/x]/[(1-x)/x]=(1+x)/(1-x)即y=(1+x)/(1-x)y(1-x)=1+xy-yx=1+xyx+x=y-1(y+1)x=y-1x=(y-1)/(y+1)所以y=f(1/x)的反函数为y=(x-1)/(x+1)...