名校
1 . 已知函数
,
.
(1)求函数
在区间
上的最小值;
(2)若函数
,且
的图象与
的图象有3个不同的交点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1462a1906c6bc21913902ea0e4a7ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49723fcae368064d6e4d44fa4bad1ae4.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e694d52a084565a4cc3d689d4a32e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b58435e488fb30016f2109f4ff060b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203dba0b34d75467e6a0d283d29f5ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f4ab890a5f38debf3a5ceb1648ed1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2024-01-24更新
|
274次组卷
|
2卷引用:四川省德阳市第五中学2023-2024学年高一下学期4月月考数学试题
名校
2 . (1)求值:
.
(2)已知
,化简:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69dc706705f154f03d723710e6df79d8.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c250590a07c7acdd6101359cc0d0bad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da0965558346ebb1bf35f21a345aff8.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
满足
.
(1)求
的解析式;
(2)判断
的奇偶性,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c43ec4ec48ae56356097e988e4d6ca.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
4 . 已知函数
是定义在
上的奇函数.
(1)求
的值;
(2)若
,
,使得不等式
成立,求
的取值范围;
(3)若函数
的图象经过点
,且函数
在
上的最大值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ccf1c969ca6fa73760cceaef52411c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4156f2c3b26fd50e368a376717b4d1ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231ede79ce34d61a836a6a8d057a831e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258158f1db73dceef6fb9ba96bad6b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ee7e039c1c08600387a62066169c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d9c0d4f95cea72aeb251d9955e6b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f8021be4db58219154d2e055203d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 计算下列各式的值:
(1)
;
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f326161fa2faefdf0ddb2a4ef03fb4bb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c31e391a0cf8b63874a0fca6710107.png)
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6 . 定义在
上的函数
满足
,且当
时,
.
(1)求
,
的值,并判断函数
的奇偶性;
(2)判断并用定义证明函数
在
上的单调性;
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40521e5866cd04cc04888b424719124c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3471484b64504fc545398f52be830010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad4c3cb38a5ce9b06167ce7217453d6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断并用定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f68c6ed09e483db6edf0b4caf5e252.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f41433bbdbb852b08b7401f3010964.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
是奇函数,当
时,
.
(1)求
的解析式;
(2)判断函数
的单调性;
(3)若方程
有三个不同的根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8672676e9dd12438f37584512c6380c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be315e528951120e7d551f654d2a1f5e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
8 . 设函数
,
.
(1)作出函数
的图象;
(2)定义
设函数
,若存在
,使得
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce427e97019745d570dd2728027fba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7947e90131a62576fd2e1374a80665cb.png)
(1)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc83eadfc25a4cd56e5034eafc7249c.png)
(2)定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3109338f9af07320479ad9e0df32617d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f034d2f18bbe75526ff320f99730e056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6073fc52cd10164c1313dd96069b8d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631a8c987ce73cebd2d3b15e2524878c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
9 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/d24822ea-be30-4efe-b9f9-bae358b30a5b.jpg?resizew=224)
(1)在坐标系下画出函数
的图象;
(2)求使方程
的实数解个数分别为
时
的相应取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163c1b38be9ba29d6446e3ddb27f4953.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/d24822ea-be30-4efe-b9f9-bae358b30a5b.jpg?resizew=224)
(1)在坐标系下画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求使方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4abe42e18da323d3147576da5ed72f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dedba68d16e6661cc981f576da4d3e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
10 . 已知定义在
上的函数
对任意实数
、
恒有
,且当
时,
,又
.
(1)求证
为奇函数;
(2)求证:
为
上的减函数;
(3)解关于
的不等式:
.(其中
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49074b2fc18e7edb1b3b6b4e6f9737c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127d6695d33a50bad7d672680b851f99.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88dd87e1476a40a3a8c44d6c886db050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a871ef7bf13de3e15489d65b57a3cc.png)
您最近一年使用:0次