解题方法
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a7e017fd21ff877b21d9d56170fe33.png)
(1)若不等式
的解集为
,求
的值;
(2)若对任意的
恒成立,求实数
的取值范围
(3)已知
,当
时,若对任意的
,总存在
,使
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a7e017fd21ff877b21d9d56170fe33.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa71f2ac3729ea7883f6ddfd2f2c9f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac55d420e554e9a8352c1523a3e0043e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449c49fa6f7adb40751a5db629162ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2dad86109e03c55b9999a4cd53d7e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0496d81c441e6cfa9c26ff7e83746eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a32fef274f43f90a37c57c46f2c670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
2 . 若区间
满足:①函数
在
上有定义且单调;②函数
在
上的值域也为
,则称区间
为函数
的共鸣区间.请完成:(1)写出函数
的一个共鸣区间________ ;(2)若函数
存在共鸣区间,则实数
的取值范围是________ .
![](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/f030c36bb8786df88d401792062a4100.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/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3daad3a31a3597f75fa109736ed2ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619473f7c43f604133c3e6d19b34fc62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03d4fd9d26992f3569b43a3a68bbcea.png)
在
上为奇函数,
,
.
(1)求实数
的值并指出函数
的单调性(单调性不需要证明);
(2)设存在
,使
成立,求出
所在的集合
;
(3)请问是否存在
的值,使
最小值为
,若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03d4fd9d26992f3569b43a3a68bbcea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854c384242ea1b47496df067cc782521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ebd84a77eb6fb88506b1d80416a0194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)请问是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b4511aee0571fe27c8a6b04a5eae68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459c84c9addfbd1cdd0a877ba7c584e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-03-28更新
|
615次组卷
|
2卷引用:安徽省六安市第二中学2022-2023学年高一上学期期末考试数学试题
名校
解题方法
4 . 对于区间
,若函数
同时满足:①
在
上是单调函数;②函数
的值域是
,则称区间
为函数
的“保值”区间.若函数
存在“保值”区间,则实数
的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e23b42cdffe75e705cf0b24763e862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.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/062f2074ff3e5e5e72e20f4d066f0e9d.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/355bda652a56449c62232febee1c8f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 函数
,已知存在实数
,
.
(1)求实数a的取值范围;
(2)讨论方程
的实根个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6cd864348d5b0dfa97f0f7a7e40ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25468da1f3cba61656a2db59b755962.png)
(1)求实数a的取值范围;
(2)讨论方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef3965ef7fbeab0f4a09cf72dc86397.png)
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6 . 已知函数
在区间
上有最大值
和最小值
,设
.
(1)求
、
的值;
(2)不等式
在
上恒成立,求实数
的范围;
(3)方程
有三个不同的实数解,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af60b2aa6227068818fa22acd23577b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9003b0c1cc1d3b70dec1065b3c4de6e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6dce06bf224e5fb0d49b1fc1b30a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7d2bb9fd6de312a742ef10c81b9b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f42aec2a770c668dc882b8bc40f423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
7 . 已知函数
,其中
.
(1)设
.若对任意实数
,
恒成立,求实数
的取值范围;
(2)是否存在实数
,使得
且
,若存在,求
的取值范围;若不存在说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7b8785da7855e62fd4a47926c16365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20a660cf7c0a3685ff01ced480883ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b7927613fdabce1a99396a0e539872.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc8d872be1982a0466c03862234eb13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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名校
解题方法
8 . 若函数
在区间
上是严格减函数,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a53297bf5b50c5484fd99279d6b043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-01-04更新
|
903次组卷
|
6卷引用:浙江省衢温“5+1”联盟2021-2022学年高一下学期期中联考数学试题
浙江省衢温“5+1”联盟2021-2022学年高一下学期期中联考数学试题(已下线)专题19 函数的基本性质 (2)上海市金山中学2022-2023学年高一上学期期末数学试题河南省信阳高级中学2022-2023学年高一上学期11月月考数学试题湖南省衡阳市第八中学2024届高三上学期开学暑期检测数学试题(已下线)期末真题必刷常考60题(22个考点专练)-【满分全攻略】(沪教版2020必修第一册)
解题方法
9 . 已知函数
.
(1)求关于
的不等式
的解集;
(2)已知函数
,若
的最小值为
,求满足
的
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883e23c0449a13d1de6d643e478b1b7b.png)
(1)求关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d99e3e25ce03391fcbb4057e79414ba.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0cffc84f149441bd0c3caaeb621ad05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cefff69077e7ffbcf63ea671d55a8013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-12-13更新
|
928次组卷
|
6卷引用:河北省保定市部分学校2022-2023学年高一上学期12月联考数学试题
河北省保定市部分学校2022-2023学年高一上学期12月联考数学试题(已下线)专题04 指数函数辽宁省辽阳市协作校2022-2023学年高一上学期期末考试数学试题(已下线)专题07 函数恒成立等综合大题归类重庆市缙云教育联盟2023-2024学年高一上学期期末数学试题(已下线)专题04 指数函数与对数函数3-2024年高一数学寒假作业单元合订本
名校
解题方法
10 . 已知二次函数
(
,
是常数且
)满足条件:
且方程
有两个相等的实根.
(1)求
的解析式;
(2)问是否存在实数
,
,使得函数
的定义域和值域分别为
和
,如果存在,求出
,
的值;如果不存在,请说明理由;
(3)令
.若方程
有三个不相等的实数根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea89fb796dea0e3e7571530eaee85bbc.png)
![](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/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec65a2bec3d4296c613a80b3ae41d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)问是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037f95b0ebd7fd758063bccd857f4ce2.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/119b20f27ee885c82edf447d24cc0cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4de786e4e59ece07c50b3adec097820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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