若f(x+1)=x2+2x则f(x)=

来源:学生作业帮助网 编辑:六六作业网 时间:2024/07/18 05:32:14
若f(x+1)=x2+2x则f(x)=若f(x+1)=x2+2x则f(x)=若f(x+1)=x2+2x则f(x)=设x+1=t,则x=t-1,可得:f(t)=(t-1)²+2(t-1)=t&s

若f(x+1)=x2+2x则f(x)=
若f(x+1)=x2+2x则f(x)=

若f(x+1)=x2+2x则f(x)=
设x+1=t,则x=t-1,可得:
f(t)=(t-1)²+2(t-1)
=t²-2t+1+2t-2
=t²-1
因此,f(x)=x²-1.

设x+1=t,则x=t-1
f(x)=(t-1)^2+2(t-1)
=t^2-2t+1+2t-2
t^2-1

f(x+1)=x2+2x
令t=x+1
那么x=t-1
f(x+1)=f(t)=x^2+2x=(t-1)^2+2(t-1)=t^2-1
即 f(t)=t^2-1
所以 f(x)=x^2-1

fx+f=4x
fx =4x-f