题干

若函数f(x)对定义域内的任意x1,x2,当f(x1)=f(x2)时,总有x1=x2,则称函数f(x)为单纯函数,例如函数f(x)=x是单纯函数,但函数f(x)=x2不是单纯函数,下列命题:

①函数 f(x)={log2xx2x1x<2 是单纯函数;

②当a>﹣2时,函数 f(x)=

x
2
+
a
x
+
1
x
在(0,+∞)上是单纯函数;

③若函数f(x)为其定义域内的单纯函数,x1≠x2,则f(x1)≠f(x2);

④若函f(x)数是单纯函数且在其定义域内可导,则在其定义域内一定存在x0使其导数f'(x0)=0.

其中正确的命题为____.(填上所有正确的命题序号)

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答案(点此获取答案解析)

①③

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