已知二次函数f(x)满足f(1+1/x)=1/x+x²+1/x²,求f(x)的解析式
问题描述：
已知二次函数f(x)满足f(1+1/x)=1/x+x²+1/x²,求f(x)的解析式
答
假设y=1+1/x x=1/(y-1) 代入 f(y)=y2-y+1/(y-1)2 y换成x F(x)=x方-x+1/(y-1)方
答
令t=1+1/x则1/x=t-1 x=1/(t-1)f(1+1/x)=1/x+x²+1/x²=t-1+1/(t-1)²+(t-1)²=t²-t+1/(t-1)²t和x同样在定义域上取值,将t换成xf(x)=x²-x+1/(x-1)²