题干

已知不恒为零的函数f(x)在定义域[0,1]上的图象连续不间断,满足条件f(0)=f(1)=0,且对任意x1,x2∈[0,1]都有|f(x1)﹣f(x2)|≤
1
3
|x1﹣x2|,则对下列四个结论:

①若f(1﹣x)=f(x)且0≤x≤

1
2
时,f(x)= 20
1
x(x﹣
1
2
),则当
1
2
<x≤1时,f(x)= 20
1
(1﹣x)(
1
2
﹣x);

②若对∀x∈[0,1]都有f(1﹣x)=﹣f(x),则y=f(x)至少有3个零点;

③对∀x∈[0,1],|f(x)|≤

1
6
恒成立;

④对∀x1,x2∈[0,1],|f(x1)﹣f(x2)|≤

1
6
恒成立.

其中正确的结论个数有(   )

A:1个

B:2个

C:3个

D:4个

上一题 下一题 0.0难度 选择题 更新时间:2019-09-05 03:17:20

答案(点此获取答案解析)

D

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