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问题 选择题
已知函数f（x）在定义域（0．+∞）上是单调函数，若对于任意x∈（0，+∞），都有f（f（x）-
1
x
）=2，则f（
1
5
）的值是（　　）
A．5B．6C．7D．8
答案

∵函数f（x）在定义域（0，+∞）上是单调函数，

且f（f（x）-

1
x
）=2，
∴f（x）-
1
x
为一个常数，

令这个常数为n，则有f（x）-

1
x
=n，①
f（n）=2，②
由①得 f（x）=n+
1
x
，③

②代入③，得n+

1
n
=2，

解得n=1，
因此f（x）=1+

1
x
，
所以f（
1
5
）=6．

故选B．

完形填空

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