名校
1 . 设
为坐标原点,定义非零向量
的“相伴函数”为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a082f57bffaa5e78978659cd089b10a0.png)
称为函数
的“相伴向量"
(1)设函数
,求函数
的相伴向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1129c691c26af951624cdc8f77ee9185.png)
(2)记
的“相伴函数"为
,若方程
在区间[0,2
]上有且仅有四个不同的实数解,求实数
的取值范围;
(3)已知点
满足
,向量
的“相伴函数”
在
处取得最大值,当点
运动时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abe13236ff4d89b1a57f63ae13013a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a082f57bffaa5e78978659cd089b10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976d4f7d71c54315b93cdba3bb07ae51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a082f57bffaa5e78978659cd089b10a0.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53de4d11d0fb3276b965dededa0043a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1129c691c26af951624cdc8f77ee9185.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d44607cab59b965b38de6022de5011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4210d67016b3e1b94920f5df6f83811b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8aa5c37c244cc7dfe7676bd3098ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ccc0712689ded371154a2ce015b13d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1129c691c26af951624cdc8f77ee9185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e0e24323fe73e5d9fc6136219306da.png)
您最近一年使用:0次
2021-09-02更新
|
1190次组卷
|
3卷引用:四川省成都外国语学校2021-2022学年高一下学期3月月考数学试题
名校
2 . 对于函数
,若
,则称
为
的“不动点”,若
,则称
为
的“稳定点”,函数
的“不动点”和“稳定点”的集合分别记为
和
,即
,
,那么,
(1)求函数
的“稳定点”;
(2)求证:
;
(3)若
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50eeb6825be5713c9d20584b74ebbd31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b164ca7a43db8ed2958a9a9b5a21369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abc439157cfc393ae61ef2eb94de1d2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab22b332a513ec60921ef348bbf8af4.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cfbcb3096b081cbf61de09879dc42ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51f8b39b8e400ac07dd8b4316df33e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-10-25更新
|
889次组卷
|
5卷引用:四川省成都市嘉祥教育集团2023-2024学年高一上学期期中考试数学试题