真题
1 . 已知集合M是满足下列性质的函数f(x)的全体:存在非零常数T,对任意x∈R,有f(x+T)=T•f(x)成立.
(1)函数f(x)=x是否属于集合M?说明理由;
(2)设函数f(x)=ax(a>0,且a≠1)的图象与y=x的图象有公共点,证明:f(x)=ax∈M;
(3)若函数f(x)=sinkx∈M,求实数k的取值范围.
(1)函数f(x)=x是否属于集合M?说明理由;
(2)设函数f(x)=ax(a>0,且a≠1)的图象与y=x的图象有公共点,证明:f(x)=ax∈M;
(3)若函数f(x)=sinkx∈M,求实数k的取值范围.
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2016-12-04更新
|
417次组卷
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5卷引用:2015-2016学年安徽省合肥市一中高一上学期期末数学试卷
2 . 已知函数
是定义域为
,且
同时满足以下条件:
①
在
上是单调函数;
②存在闭区间
(其中
),使得当
时,
的取值集合也是
.则称函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
是“合一函数”.
(1)请你写出一个“合一函数”;
(2)若
是“合一函数”,求实数
的取值范围.
(注:本题求解中涉及的函数单调性不用证明,直接指出是增函数还是减函数即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
②存在闭区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94fb4381c862741460ce202614b463f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6be67cbce81d7e50115e040bcd3dba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6be6995efb149bafaba4a3bf804870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ecf481b6b83aa59a2befd7c4bfdbf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4f8a9523ddd677b301da71ec4e89d0.png)
(1)请你写出一个“合一函数”;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54c221d55939413899ca82229b702d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(注:本题求解中涉及的函数单调性不用证明,直接指出是增函数还是减函数即可)
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