题目

已知f(2x+1)=x²-2x,则f(根号2)=

提问时间：2020-10-30

答案

令t=2x+1,则x=(1/2)(t-1)
则
f(t)=(1/4)(t^2-2t+1)-(t-1)
=(1/4)(t^2-6t+5)
=(1/4)(t-1)(t-5)
所以
f(x)=(1/4)(x-1)(x-5)
则
f(x)=(1/4)(√2-1)(√2-5)
=(1/4)(7-6√2)