名校
1 . 已知函数
.
(1)若
,是否存在a
,使
为偶函数,如果存在,请举例并证明,如果不存在,请说明理由;
(2)若
,判断
在
上的单调性,并用定义证明;
(3)已知
,存在
,对任意
,都有
成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e73422d2197a5a71769436381b7229.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c1fd1da3a9e6465bb3b66894120b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5500ad00466c3f2ff8ba691f2653e6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd456469aaa6dafb1e275183d217435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4438620ff101b83aef035104db1a6e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a1f815b0e0b6516b684a93e1850667.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e424a9e6b2505aad5eb944b00f5222bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76d0c6032c22c5d435968f414e506cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9956260c9412f340df7addda6707f3.png)
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2022-03-14更新
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1233次组卷
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3卷引用:湖南省长沙市第一中学2021-2022学年高一下学期入学考试数学试题