解题方法
1 . 已知定义域为
的函数
满足对任意
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e378c159436eb968d2b03eedd0e67657.png)
(1)求证:
是奇函数;
(2)设
,且当
时,
,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff68d7374e6f548d902f18ed6b6e8c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243a45670e2b2fe44496d3244ed5a68d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e378c159436eb968d2b03eedd0e67657.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527a896aec4a245945e5edee00deed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e800115ee291759e0dbc95fdc43b2.png)
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名校
2 . 计算:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25653a62f8dbaa1c50f31d88d9df2ae2.png)
(2)已知
,试用
表示
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25653a62f8dbaa1c50f31d88d9df2ae2.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d586be112cea35ce289229e22bef7dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8108229c24e88fdc0cf2302b1228b51e.png)
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3 . 对于区间
,若函数
同时满足:①
在
上是单调函数,②函数
的定义域为
时,值域也为
,则称区间
为函数
的“保值”区间.
(1)求函数
的所有“保值”区间.
(2)函数
的一个“保值”区间为
,当
变化时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57a73413293485eec898e382c345a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.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/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a1529190be96a75cc40bfd7d6b647e.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9292cd30c0ffa46bbbbb59e1a546a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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4 . 已知某产品市场供应量P满足关系式
(其中t为关税的税率,x为市场价格(单位:千元),k,m为常数).研究表明,当关税税率
时,市场供应量曲线如图所示:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/2a34ec88-ee76-4842-b5aa-f71c1aa88252.png?resizew=167)
(1)求k,m的值;
(2)若市场对此产品的需求量Q满足关系式
(其中t为关税的税率,x(单位:千元)为市场价格).规定“供求比”为供给与需求的比例.根据市场调查,当产品的供求比在0.8到1.2之间时(含0.8和1.2),供求关系较为平衡:当供求比小于0.8时,会出现供不应求的现象:当供求比大于1.2,会出现供过于求的现象,则当关税税率为
时,市场价格应在什么范围的时候,供求关系较为平衡?(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cd84c82bb36366e5673ddcf4d85bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/162f365a3215de46b7d00f7833650405.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/2a34ec88-ee76-4842-b5aa-f71c1aa88252.png?resizew=167)
(1)求k,m的值;
(2)若市场对此产品的需求量Q满足关系式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644b49d1fa2b67b3d8ff976b659addbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8761b14f861830715f4f2e3043a08f7.png)
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解题方法
5 . 已知
,
.
(1)求函数
在区间
上的最小值.
(2)对于任意
,都有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98348a6484adcce636bb7220a69d8678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a6ef2184999b10fa0193f79db45467.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(2)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e32125207addc3fdb92ceb0ec80ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2f3f41ca28e9b91f24579f7d5680a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 已知函数
.
(1)若不等式
的解集为
,求实数
的值;
(2)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75fcd8a1a345411490f0a005af928fa.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d03268e486f9fb09a44eca7d8ff7a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
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解题方法
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a5c71c05f63352b457b63d925fde34.png)
(1)是否存在实数
使得关于
的不等式
的解集为
,若存在.求实数
的值或取值范围,若不存在,请说明理由;
(2)若关于
的不等式
的解集是
,集合
,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a5c71c05f63352b457b63d925fde34.png)
(1)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc65d6eb9b63f96d80b54ec9893aee8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d462ed4ec22e8fe51f09eb30e8792532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ecd53c3a79ea63c676d238b1cd9eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc887a6c34c3e2f859e6a59a9ed4cac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c4ba74adbcdc3cba5a727b4e7886c2.png)
为定义域上的奇函数.
(1)求实数
的值;
(2)若
,试用
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c4ba74adbcdc3cba5a727b4e7886c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb76c52881250e22807c5fcc8ba90188.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd876870cd37988b925e9b0de68bd4d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c3681bdf05d46ca21f13f42bf9423d.png)
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解题方法
9 . 已知函数
.
(1)若
,判断
在
上的单调性,并用单调性的定义证明;
(2)设函数
,若对任意
,总有
,使得
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f44e619b41991f2002cc203be8d6f3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189b2da6c420bf8f8900002d14f65f72.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2773b25d35138dad01fadf8632f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d5a5e70f64f0933ae1e4ddec5fa2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92a39100a738af90edc8da0fc3c5b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347ac85769012f89d1f9951684e1d7b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-21更新
|
457次组卷
|
2卷引用:江西省上饶市广丰区大千艺术学校2023-2024学年高一上学期期末数学试题
解题方法
10 . 近几年,直播平台作为一种新型的学习渠道,正逐渐受到越来越多人们的关注和喜爱.某平台从2020年建立开始,得到了很多网民的关注,会员人数逐年增加.已知从2020到2023年,每年年末该平台的会员人数如下表所示(注:第4年数据为截止到2023年10月底的数据).
(1)请根据表格中的数据,从下列三个模型中选择一个恰当的模型估算该平台建立
年后会员人数y(千人),求出你所选择模型的解析式,并预测2023年年末的会员人数;
①
;②
(
且
);③
(
且
);
(2)为了更好的维护管理平台,该平台规定第x年的会员人数上限为
千人,请根据(1)中得到的函数模型,求k的最小值.
建立平台第x年 | 1 | 2 | 3 | 4 |
会员人数y(千人) | 28 | 36 | 52 | 82 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304b2af2e9b972ed2637dc5cd9bf2a3e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de07bfd93213360aae1620ba41a9a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177221206acd5fbb4c69e771d37c6033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2015b8dd73e9ab0eae4a13dd591d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1538ef1738d41669997db2da1d5a275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(2)为了更好的维护管理平台,该平台规定第x年的会员人数上限为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8066bd8da6de9932769e336360a6cb.png)
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