名校
1 . 设函数
,函数
.
(1)若函数
为奇函数,求a;
(2)若
,判断并证明函数
的单调性;
(3)若
,函数
在区间
上的取值范围是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6fe56c70ed96e7f0ee48063dae9fc7.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b605bf480dc152b67ebb9ebd96200b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8ffc84689f8573e0b641d641f895e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
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2021-11-23更新
|
403次组卷
|
2卷引用:山东省青岛市青岛第五十八中学2021-2022学年高一上学期期中数学试题
名校
解题方法
2 . 已知函数
的定义域为D,且
同时满足以下条件:
①
在D上是单调递增或单调递减函数;
②存在闭区间![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
D(其中
),使得当
时,
的取值集合也是
.那么,我们称函数
(
)是闭函数.
(1)判断
是不是闭函数?若是,找出条件②中的区间;若不是,说明理由.
(2)若
是闭函数,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/4fe7d5809da02c15a43a0e9a898b9086.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②存在闭区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b980d8446f130dfc405c196109e73ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70128385b9ab66ac44614af35a0dcdce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e16b22f8a70465aacea1cc8878777eb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50254ea7b079bc99aa41ad6e79252df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,且对
,
,都有
.
(1)求
的表达式;
(2)已知关于x的不等式
的解集为A,若
,求实数a的取值范围;
(3)已知数列
中,
,
,记
,且数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282e825c14110833c45ac9db52e5f42c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f370a1d4dd341e5ab1774a66c66c1204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845ebe200c96e5259501ad8978ffae5f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6b1cfb0b2755e419ed28cbb4d0ece4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6397b02d758108ce97907d2efcac1d63.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2bc260323ce13981f2ee3fdfb52d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d08ed7d51b6175cae1cbc40e8878e3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29877f249cacfa421cc082410a73e69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d35a29be4e48c56ee056c4b9cad8110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5737f1f9cad2471f3ca53241b25a1eb9.png)
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解题方法
4 . 对于定义域为
的函数
,如果存在区间
,同时满足:
①
在
上是单调函数;
②当定义域是
时,
的值域也是
.
则称
是该函数的“等域区间”.
(1)求证:函数
不存在“等域区间”;
(2)已知函数
(
,
)有“等域区间”
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5313c921defe84689aefde4773ad2b56.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
②当定义域是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
则称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243881c59e5d46fbf1335d115cab85b7.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9bb4ac41d47897720ee8f6c86cc261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次