解题方法
1 . 已知函数
,
.定义
,设
,
,
为常数.
(1)当
时,判断函数
的奇偶性;
(2)定义区间
的长度为
.若
的解集为
,问是否存在
,使得
的全部区间长度之和等于6,若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df18da1ecd1a83afc4544ee71f00c56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92fd3003a50fc4b754f134fe799b12a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726263a79bec039dd073ff799e52eca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647a44d40e8b50a9c308541bbe646dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
(2)定义区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701fce58a3087d253fd4fa948030eb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ed2fb4a6389a9994694ba9aa5e6422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2 . 已知函数
,其中
.
(1)若
,求
的值;
(2)当
时,
(i)根据定义证明函数
在区间
上单调递增;
(ii)记函数
,若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a6dd8adbd012e53a6a0dcf700a3696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b1ec158439b8c797514d254b7944c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(i)根据定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189b2da6c420bf8f8900002d14f65f72.png)
(ii)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75317d3103b38929dd80b11d71cd16b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ceab8557090b27ebd974d579723594b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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3 . 设函数
,其中
.
(1)若
,求
在
上的最大值;
(2)已知
满足对一切实数x均有
,求函数
的值域;
(3)若
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97306b2fb2023559e74fd632d4325ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0729eb6f1f14582b37b5cdcdda2c5c5a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c01ef6036d39379287b6444b3446ada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d19e8dd827a3c1a4dea84f385b02813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd95ae33c06d271d7e1fe1557a707e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9085a9b1ceed4ab947c21669e85c5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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真题
4 . 设
,画出函数
的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7749fa0f912c0b031a9bee26e5f00261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9acbadd39bc954fb82331f1752a27a.png)
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2022-11-09更新
|
332次组卷
|
2卷引用:河南省南阳市邓州春雨国文学校2023-2024学年高二上学期8月月考数学试题
5 . 已知函数
的图象经过点
,其中
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/a81b6dc8-3d74-461c-a93d-565dc984fed5.png?resizew=304)
(1)若
,求实数
和
的值;
(2)设函数
,请你在平面直角坐标系中作出
的简图,并根据图象写出该函数的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d05f71af920f17cce15975c7ce3021bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac7c28099bfbb7dc2a45ad166eace05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810949b76573ccd9d43af3815299d443.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/a81b6dc8-3d74-461c-a93d-565dc984fed5.png?resizew=304)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a700ff22bb44210b352a6c1d3356d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55bc9d46e8aea1076ff0adad3f73943c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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2022-09-11更新
|
272次组卷
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2卷引用:福建省泉州市第六中学2021-2022学年高二下学期期中模块测试数学试题
名校
解题方法
6 . 已知函数
.
(1)当
,且
时,求
的值;
(2)若存在实数
,使得函数
的定义域为
时,其值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870a7e1c6303c19ce3e86368ee2f8f21.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)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47af1ee63d6925c4cb2b6ede44c5669.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/ad8af7bed124f00c8e19b52d028b4d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
7 . 已知函数
,其中实数
.
(1)当
时,
的最小值为2,求实数a的值.
(2)记
,设
,若
恒有解,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14275d11fea7cb0df61a50f8415bb1b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095c5f7a3c6917839c01fd1e5654ee91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe32b32e32d59155649fe6e1979201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f66fd3129db024daf48dfd8c4673a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f2b3006c8a2784e51e57e30e22ea9e.png)
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2022-06-25更新
|
443次组卷
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5卷引用:浙江省温州市十五校联合体2021-2022学年高二下学期期末联考数学试题
浙江省温州市十五校联合体2021-2022学年高二下学期期末联考数学试题河北省廊坊市第十五中学2022-2023学年高一上学期第二次月考数学试题(已下线)专题02 恒成立、能成立问题 (1)(已下线)专题3.6 函数的概念与性质全章八类必考压轴题-举一反三系列山东省烟台市中英文学校2023-2024学年高一上学期期中考试数学模拟试题
名校
8 . 对于函数
,若存在正常数
,使得对任意的
,都有
成立,我们称函数
为“
同比不减函数”.
(1)判断函数
是否为“
同比不减函数”?并说明理由;
(2)若函数
是“
同比不减函数”,求实数
的取值范围;
(3)是否存在正常数
,使得函数
为“
同比不减函数”?若存在,求
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2ab09ce6ffc17ccbe9d4b203009d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a65456221e249dd2aa9a775e32edd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03cddfaa4522ab14daa358d2d5af019e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)是否存在正常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d05006c96efba795fea69523172b7a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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2022-04-22更新
|
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4卷引用:上海市嘉定区第一中学2023-2024学年高二上学期10月月考数学试题
上海市嘉定区第一中学2023-2024学年高二上学期10月月考数学试题上海市控江中学2021-2022学年高一下学期期中数学试题(已下线)第一章 导数与函数的图像 专题三 导数中常见函数的图像 微点4 导数中常见函数的图像及其性质(四)上海市育才中学2023-2024学年高一下学期期中质量检测数学试卷
名校
解题方法
9 . 已知函数
.
(1)当
,且
时,求
的取值范围;
(2)是否存在正实数a,
,使得函数
在
上的取值范围是
.若存在,则求出a,b的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5663c187aa4e5fdfd1dd28895872ce37.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/82e9085aa49e1771ddcd9c327aba486b.png)
(2)是否存在正实数a,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f9fcab2886322d40bb5b52d997984fe.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/9c80c2b55996f6735f5089581f632672.png)
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2022-02-27更新
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名校
10 . 对于函数
,若在定义域内存在实数
,满足
,则称
为“
类函数”.
(1)设
是定义在
上的“
类函数”,求实数
的最小值;
(2)若
为其定义域上的“
类函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a17feb50e8b343fb854143b391774e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae146fc71a20938bd37b962b016c5ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebb595f7dfe7b4a86413b5bd99535c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2021-09-10更新
|
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