名校
1 . 已知函数
.
(1)求实数
的值,使得
为偶函数;
(2)当
为偶函数时,设
,若
,都有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbadafc438a3f015db437db7a47c3139.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6af5876f5e5cda0f31cca886bf0fbe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87008291cdba83461d58dbc9426d777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aecb3e0e056d5953fe58f5fb02f637c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-01-18更新
|
492次组卷
|
3卷引用:福建省莆田市2023-2024学年高一上学期期末数学试题
2 . 已知奇函数
,且
的图象过点
.
(1)若
,
恒成立,求实数
的取值范围;
(2)是否存在实数
,使函数
在区间
上的最大值为1.若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e678d4160d600c868f95d09fac8bcae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de261e9b4defbc0be6440397031a87b8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4affadb1c6c71548e7faa459f967f4d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ea50fab6d97d24a49dedb5ea356b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307d5e418315e464160389b14cd8f319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef1f2d3246ca24d9eec31e2b4894605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
3 . 近几年,随着网络的不断发展和进步,直播平台作为一种新型的学习方式,正逐渐受到越来越多人们关注和喜爱.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,该平台会员每年年末的人数如下表所示(注:第4年数据为截止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建立该平台
年后平台会员人数
(千人),求出你所选择模型的解析式,并预测2023年年末会员人数:
①
,②
(
且
),③
(
且
);
(2)为了更好的维护管理平台,该平台规定会员人数不能超过
千人,请根据(1)中你选择的函数模型求
的最小值.
建立平台第![]() | 1 | 2 | 3 | 4 |
会员人数![]() | 28 | 40 | 58 | 82 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304b2af2e9b972ed2637dc5cd9bf2a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0bed76927f9a798529ce101f285b71.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,该平台规定会员人数不能超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1861f0d677c8473bdc56530d7be9b8b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2024-01-09更新
|
550次组卷
|
3卷引用:福建省福州市九师教学联盟2023-2024学年高一上学期1月联考数学试题
名校
解题方法
4 . 已知函数
(
且
)在区间
上的最大值与最小值之和为20,记
.
(1)求a的值,并证明:
;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602f0dcb6d14064cf4903f3fceed10ff.png)
(1)求a的值,并证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2493344c3e6aa5e038c98ee6d60bb62d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cdf222081c65e6b545d9342603b508.png)
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解题方法
5 . 已知
,
,其中
,
.
(1)当
时,解不等式
.
(2)设
,若
,
,恒有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9786c92b53010f3722ad0b7eae513c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e642b6edc818fa867ae42501d9d39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9652e30dad4d1ea51c10b229a10252d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cdd2fd083206898c871d1c7e9ea7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95074efb856e136b4a349abc8c2186a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3326078a8773562e58826a1a110e31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 定义域为
的函数
满足
,
,若
时,
恒成立,则实数
的取值范围是( )
![](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/322eb46d949b9580bcc057d146b7fc58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9dceef7e01934235245bc9a5df3861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a07ea4aaaf82f4f2a54df7673504df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43758e8f118028e1bb65f35f222ae68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-12-14更新
|
182次组卷
|
2卷引用:福建省龙岩市连城县第一中学2023-2024学年高一上学期月考2数学试题
名校
解题方法
7 . 已知不等式
对任意实数
恒成立,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98378c6423dd990862e48fe80c7e3fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
8 . 已知函数
.
(1)
时,判断
的奇偶性,并证明;
(2)若对任意
,总有
成立,其中
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db04bee3cf15e611c7d075e94c81f3c2.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd85d4af7dfca7633dd9ca7993ec4d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcaaae224dc99877affb7c3213b83382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6cf6b0f57200e88644e7b851c6e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . 已知定义在
上的函数
.
(1)若函数
在
上单调递增,求实数
的取值范围;
(2)若函数
的定义域内存在
,使得
成立,则称
为局部对称函数,其中
为函数
的局部对称点.若
是
的局部对称点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c39fe984666f2661aa281c3d18865a.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5f835d9cbbdcb063bdfeed0a9079e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.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
2023-11-14更新
|
749次组卷
|
4卷引用:福建省厦门市厦门大学附属科技中学2023-2024高一上学期12月阶段测试数学试题
名校
解题方法
10 . 已知函数
是定义域为
的奇函数.
(1)求实数
的值;
(2)若
,不等式
在
上恒成立,求实数
的取值范围;
(3)若
,且函数
在
上最小值为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc380c71c702006389018511f7c373e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f3df8bf24d2c68add3f3de3efc4147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6e82456f711d428f237d9b31ab04f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132d41feaf28a5d96470d23780262b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56fbec93189276445b83c6df4e9f4866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c7b06034ba574b0e94f4b6cb59308a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次