名校
1 . 已知函数
,给出下列四个结论:
①函数
是奇函数;
②
,且
,关于x的方程
恰有两个不相等的实数根;
③已知P是曲线
上任意一点,
,则
;
其中所有正确结论的序号是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b911ca0a9600ca9e5b657e2c2cac6742.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56fe84600ef7b977bc3eeb9a4f0252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278d3bdd40c4386b93e0ef5b91009094.png)
③已知P是曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e193e00a5d2b4654735c1f850d9dc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b4c42a51640b900ca9f26db1b1eff0.png)
其中所有正确结论的序号是
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解题方法
2 . 设函数
的定义域为
,且满足
,则不等式
的解集是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc4679a8360516b33a3cb9e86ab25b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390c620c0fd4a2cd8622171bdaf05f5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ec6c59e1ce704a29d76726e2674129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd1f61519643b2a62367079f19c6c22.png)
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3 . 已知函数
.
(1)当
,且
时,求
的值;
(2)若存在区间
(
为函数定义域),使
在区间
上的值域也为
,则称
为
上的精彩函数,
为函数
的精彩区间.求
是否存在精彩区间?如不存在,说明理由;
(3)若存在实数
使得函数
的定义域为
时,值域为
,则称区间
为
的一个“罗尔”区间.已知函数
存在“罗尔”区间,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/370efb70486b9964df67552cb7734ec5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba934874cc9f2ab272fdff67ea23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7266b2ef457b8ddeee3fa2cc24022e.png)
(2)若存在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0195f699765021e2c6ea985e487971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9dbaef457ca0cad2815d03a17e5d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030052a6936e5136de625c65eea375af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.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/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
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4 . 已知函数
且
的图象经过
.
(1)设函数
,求
的定义域;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e02a79afeda26fa2425183f26c15fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3323e8343c7319d5a1fa4894d1f6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e632cc082fec1d04b5665d2d46609d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-12-09更新
|
423次组卷
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2卷引用:四川省眉山第一中学2022-2023学年高一上学期第三次月考数学试题
名校
解题方法
5 . 已知函数
的定义域为
,其中
为实数.
(Ⅰ)求
的取值范围;
(Ⅱ)当
时,是否存在实数
满足对任意
,都存在
,使得
成立?若存在,求实数
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22008acfa391c7b0f7f0cb593c65667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a3163cc2d37e7b7fe450f6e8bf8500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a3de2dbd396b0b8d1929eb9b634d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021-01-30更新
|
1259次组卷
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5卷引用:四川省成都市2020-2021学年高一上学期期末数学试题
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6 . 对于定义在区间
上的两个函数
和
,如果对任意的
,均有不等式
成立,则称函数
与
在
上是“友好”的,否则称为“不友好”的.
(1)若
,
,则
与
在区间
上是否“友好”;
(2)现在有两个函数
与
,给定区间
.
①若
与
在区间
上都有意义,求
的取值范围;
②讨论函数
与
与在区间
上是否“友好”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](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/5a56806c9bf7927769af420fdabe96cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc69dd6b191f31ea8d87f867a456a4a.png)
![](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/57b85a97933a1d984f6e484b4021c800.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b034f42a44cb15e6b320f24dd7cdd0f.png)
![](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/b6c1756b564bf1d998d8179637011c88.png)
(2)现在有两个函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69912d099cb8fd2fffdf32b2cae06a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc39fe82ee20b0554e439a6a9234be19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221f9c828a6de90bcae98354634a8ad5.png)
①若
![](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/221f9c828a6de90bcae98354634a8ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②讨论函数
![](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/221f9c828a6de90bcae98354634a8ad5.png)
您最近一年使用:0次
2020-05-09更新
|
1856次组卷
|
6卷引用:四川省泸州市泸县第五中学2020-2021学年高二上学期开学考试数学(理)试题
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名校
7 . 已知:函数
,
.
(1)若
的定义域为
,求
的取值范围;
(2)设函数
,若
,对于任意
总成立.求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc90719c0078d2a9dd6590b9ba55bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fda90490b6b98cb1f0878b0cace041.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a20457d180264f78d611dc7893d735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989f8bd34cd1acecae079e1bc244d64b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ea6baecc58836834dff78b68bf09cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-05-08更新
|
769次组卷
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解题方法
8 . 已知函数
的定义域为
.
(1)求实数
的取值范围;
(2)设实数
为
的最大值,若实数
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f17d73da0771080cb4373e63aead0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47eb8fb6bc2ea326b95ad9526eb00520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2b6d055bcefa3e6ff4da5d2096805b.png)
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2020-04-14更新
|
1073次组卷
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11卷引用:四川省宜宾市叙州区第二中学校2019-2020学年高三下学期第二次月考数学(理)试题
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9 . 已知函数
的图象与函数
的图象关于直线
对称.
(1)若
,求实数
的值;
(2)若函数
的定义域为
,值域为
,求实数
,
的值;
(3)当
时,求函数
的最小值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679da8a975f3a340f456d205b9da9a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0964e64eca750b956d0dbf06ca3593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa76864be3da2395f315fd1b7c9da209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f98f77cce9027d6b58ca0e3868e94ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119b20f27ee885c82edf447d24cc0cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a1c1f0951b6032791da53d313449d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a90170d7ef5ff6d1d63517c166f7a9.png)
您最近一年使用:0次
2020-01-29更新
|
462次组卷
|
2卷引用:四川省绵阳市江油市江油中学2022-2023学年高二下学期期末数学文科试题
解题方法
10 . 设
且
,函数
,两函数的定义域分别为集合
,若将
.
(1)试求函数
在
上的单调性;
(2)若
,函数
在
上的值域恰好为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e7581a9b1bdf7e15be780aaaecc4a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2591474c35ae00ca5a402a654e45079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57d6b8895d2791434d2aa84c344c69e.png)
(1)试求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5313c921defe84689aefde4773ad2b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc402f843459c40b8a24113590e27e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2016-12-03更新
|
425次组卷
|
2卷引用:四川省遂宁市绿然教科院2021-2022学年高一上学期期末联考数学试题