名校
解题方法
1 . 已知函数
在
上有意义,且对任意
满足
.
(1)求
的值,判断
的奇偶性并证明你的结论;
(2)若
时,
,判断
在
的单调性,并说明理由.
(3)在(2)的条件下,请在以下两个问题中任选一个 作答:(如果两问都做,按①得分计入总分)
①若
,请问是否存在实数
,使得
恒成立,若存在,给出实数
的一个取值;若不存在,请说明理由.
②记
表示
两数中的较大值,若对于任意
,
,求实数
的取值范围?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c275d203295b989c129101d82e74ae01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f97718f1472e11502eaa775b58bd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608fd0dfd30079f4337ef571571eb287.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afeede1e920a57feb40fc0cd66b961a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7baa4f3372e6a0aa38056e0de3b0fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6000b174147cec2de26041837aec1b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c275d203295b989c129101d82e74ae01.png)
(3)在(2)的条件下,请在以下两个问题中
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad3411b2f63b59dafb6fccdacddd1fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32f78e3f288a433f8ba3661e551af4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eabe40ebe23d91aa1447b9896b300f83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287376282d8c04d267ec6add486853f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd851ca08ce2b6224e9d5e9952cff60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2021-12-12更新
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917次组卷
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2卷引用:北京师范大学附属中学2021-2022学年高一上学期期中考试数学试题