名校
1 . 已知函数
,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740ed15c8e90b5ef3b7f36a8d94ae82f.png)
A.![]() ![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
2 . 已知定为域为R的函数
满足:
为偶函数,
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e356a6e54a669fda721085096c8416db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b568b2cee9ef2a32d2f27305a9104d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca81dd8e6716f5ba65d489cbf5ea4f21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7852e7c81e0f97dad6ae5551bf7152f.png)
A.0 | B.1 | C.2 | D.3 |
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3 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b652e9ae697aaf83d3f13ac97cae308.png)
(1)若
的值域为
,求满足条件的整数
的值;
(2)若非常数函数
是定义域为
的奇函数,且
,
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853f9db73ed0b83a813c645758d6e56d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b652e9ae697aaf83d3f13ac97cae308.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de0b2aa451ca49b289b5ce99dbbb1ad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若非常数函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924e2a44ebdbd85a75cba44bc24149c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f464c14d28814ee9c1b7a744da92a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319aea6ba5f3e2445a054141c47b0d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f33fa4634d68fd772d6360f1415862c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-03-19更新
|
376次组卷
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8卷引用:陕西省西安市高新第一中学2023-2024学年高一下学期第二次月考数学试题
陕西省西安市高新第一中学2023-2024学年高一下学期第二次月考数学试题河北省邢台市五岳联盟2024届高三上学期9月月考数学试题江西省部分高中学校2024届高三上学期9月大联考数学试题河南省2023-2024学年高三上学期一轮复习阶段性检测(三)数学试题(已下线)专题4.7 指数函数与对数函数全章八类必考压轴题-举一反三系列(已下线)6.3 对数函数(2)-【帮课堂】(苏教版2019必修第一册)(已下线)专题2.3 幂函数与指、对数函数【九大题型】黑龙江省大庆铁人中学2023-2024学年高一下学期开学考试数学试题
4 . 若函数
满足
,当
时,
,若在区间
上,
有两个零点,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8df1f1dbc0a2e8b771f17cb59738c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84d41b94678bd8e3c114f40adb5425c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab166615f6a41dd151115392bcbdbf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
5 . 已知
是定义在
上的函数且
图象关于点
对称,
是偶函数,若当
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5215a578933ba72022450a6d3a37d14.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc391884cb2d4e69c318015ed1cc5724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5215a578933ba72022450a6d3a37d14.png)
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解题方法
6 . 已知函数
恰有3个零点,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d14ccd94ab1a850796e0a9bd3e6b6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-12-27更新
|
338次组卷
|
4卷引用:陕西省西安市部分学校2024届高三上学期12月联考数学(文)试题
名校
解题方法
7 . 已知函数
(
,且
).
(1)若函数
的图象与函数
的图象关于直线
对称,且点
在函数
的图象上,求实数
的值;
(2)在(1)的条件下,不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e349f49908801a73999320f7a49820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e232f88382623f0f68d56dcdc162a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)在(1)的条件下,不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd74fd1f0b78c02388c5a37ff91b7ce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b7924a628b9cd9fd6d5f38ee744419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 . 已知函数
与
具有如下性质:
①
为奇函数,
为偶函数;
②
(常数
是自然对数的底数,
).
利用上述性质,解决以下问题:
(1)求函数
与
的解析式;
(2)证明:对任意实数
,
为定值;
(3)已知
,记函数
的最小值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df412ae6aa217d7eaa8dd3b88faa9b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
利用上述性质,解决以下问题:
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)证明:对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c55cc1394290408de681b3e23865ca.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647f47ff99c3aadb742b07fc39c7ad7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4b8114fcc770a8512cf03da137ca4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4b8114fcc770a8512cf03da137ca4e.png)
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名校
9 . 在函数定义域内,若存在正实数
,使得函数在区间
上的值域为
则称此函数为“
档类正方形函数”(其中
),已知函数
.
(1)当
时,求函数
的值域;
(2)当
时,是否存在
,使得函数
为“
档类正方形函数”?若存在,求出实数
的取值范围,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a6162adc13ebe4c5cd3df7d5176d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e151310fd02cd9c47e8892609ddde1c5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2e48341bf9ce1d6ba26b31616f97b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
10 . 已知
是定义在
上的不恒为零的函数,对于任意
都满足
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab4b75fa22deba7fcbcdcb31dd45b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db13144a4b27bc76c6ca989423fe95e7.png)
A.![]() |
B.![]() |
C.若![]() ![]() |
D.若当![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-11-19更新
|
1077次组卷
|
7卷引用:陕西省西安市铁一中学2023-2024学年高一上学期第二次月考数学试题