设f(x)=x5-5x4+10x3-10x2+5x+1,则f(x)的反函数f-1(x)=_.

问题描述:

设f(x)=x5-5x4+10x3-10x2+5x+1,则f(x)的反函数f-1(x)=______.

∵y=x5-5x4+10x3-10x2+5x+1=(x-1)5+2,
∴x=(y−2)

1
5
+1,
∴f(x)的反函数f-1(x)=
5 x−2
+1

故答案为:
5 x−2
+1