已知定义域为{x/x∈R,且x≠1}的函数f(x)满足f(1/1-x)=1/2 f(x)+1,则f(3)=?

题目

已知定义域为{x/x∈R,且x≠1}的函数f(x)满足f(1/1-x)=1/2 f(x)+1,则f(3)=?

答案

由f(1/1-x)=1/2 f(x)+1,得f(3)=1/2f(2/3)+1 ①f(2/3)=1/2f(-1/2)+1 ②f(-1/2)=1/2f(3)+1 ③由①②③得2f(-1/2)-2=1/2[1/2f(-1/2)+1]+1等价于7f(-1/2)=14∴f(-1/2)=2又由③,得f(3)=2f(-1/2)-2=2*2-2=2...