名校
解题方法
1 . 已知函数
.
(1)求证:函数
是
上的减函数;
(2)已知函数
的图像存在对称中心
的充要条件是
的图像关于原点中心对称,判断函数
的图像是否存在对称中心,若存在,求出该对称中心的坐标,若不存在,说明理由;
(3)若对任意
,都存在
及实数
,使得
,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4077e55784510b6adc6a040daa85eb18.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c86212cfe7338ae7adca7d58eca15fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b3ed9c4fa3bce5d45202695bbc179d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55e9f87ebd16be23db0e9fea26da11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e9fc70929247a1cdc2e8fc5c83df2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-12-20更新
|
727次组卷
|
4卷引用:江苏省常州市前黄高级中学2023-2024学年高三上学期期初考试数学试题
名校
解题方法
2 . 已知函数
是
上的偶函数,当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d7211d89e2d825df0024a298175d2f.png)
(1)当
时,求函数
的解析式;
(2)用单调性定义证明函数
在区间
上是单调增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a28068770a85b88b42321cd71ecd3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d7211d89e2d825df0024a298175d2f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用单调性定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9414348d57c7fc77dcfa8f0744cb0c9.png)
您最近一年使用:0次
解题方法
3 . 已知函数
是定义在
上的偶函数,当
时,
.
(1)当
时,求函数
的解析式;
(2)用定义证明函数
在区间
上是单调增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a28068770a85b88b42321cd71ecd3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5dbfac684b9901a16ae61dbaa0f817.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)用定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
您最近一年使用:0次
2022-03-30更新
|
173次组卷
|
3卷引用:江苏省常州市八校2021-2022学年高一上学期12月联考数学试题
江苏省常州市八校2021-2022学年高一上学期12月联考数学试题(已下线)期末测试卷02(基础卷)-【满分计划】2022-2023学年高一数学阶段性复习测试卷(苏教版2019必修第一册)天津市实验中学滨海学校2023-2024学年高一上学期期中数学试题
名校
解题方法
4 . 已知不等式
的解集为
.
(1)求
、
的值,
(2)若
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51acab82bc9179698145f7e834720a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194d49965dad3d8a71a2edbf3ae4fdc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a62d8481c22c7b43ffe891ae5b30b089.png)
您最近一年使用:0次
2022-09-19更新
|
634次组卷
|
3卷引用:江苏省常州市平陵高级中学2022-2023学年高三上学期期初测试数学试题
名校
解题方法
5 . 一个完美均匀且灵活的平衡链被它的两端悬挂,且只受重力的影响,这个链子形成的曲线形状被称为悬链线(如图所示).选择适当的坐标系后,悬链线对应的函数近似是一个双曲余弦函数,其解析式可以为
,其中
,
是常数.
![](https://img.xkw.com/dksih/QBM/2022/2/20/2920729377693696/2933744408739840/STEM/ff7d97faa9394cac85c62366ae557088.png?resizew=202)
(1)当
时,判断并证明
的奇偶性;
(2)当
时,若
的最小值为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49757d6d62b9c313b11aafd537475845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://img.xkw.com/dksih/QBM/2022/2/20/2920729377693696/2933744408739840/STEM/ff7d97faa9394cac85c62366ae557088.png?resizew=202)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0b38c8ec2cf6a3b999dd2f851179cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1c15263cbb460891a4af6a9c693060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/007a2c5b15ecfabfb01e8d2c0f5793bd.png)
您最近一年使用:0次
2022-03-11更新
|
200次组卷
|
2卷引用:江苏省常州市前黄高级中学2023-2024学年高三上学期期初考试数学试题
名校
解题方法
6 . 已知函数
是奇函数,且
.
(1)求函数
的解析式,并判定函数
在区间
上的单调性(无需证明);
(2)已知函数
且
,已知
在
的最大值为2,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73548a59ff2f603a2ea60c570dac3fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed670b1f668778c6243f3f7470ee7d2.png)
(1)求函数
![](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/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03538af361c7399596c54fb6bf69ba79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94560057a020418920b925307ccf6afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad814089e37543b2f547af9ae75b6dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
您最近一年使用:0次
2022-03-09更新
|
463次组卷
|
5卷引用:江苏省常州市北郊高级中学2022-2023学年高二上学期期初调研数学试题
7 . 已知函数
定义域为
,且函数
同时满足下列
个条件:①对任意的实数
,
恒成立;②当
时,
;③
.
(1)求
及
的值;
(2)求证:函数
既是
上的奇函数,同时又是
上的增函数;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](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/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6f5d45adf0314f93a495f037109bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c24244b1fdbf1455087c2ebf41c8b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32822a106d217ffdec43557a236f786.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd2c5760181b2c974811564b55b65f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89da974e3d5186a8dfb0780461248a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2022-02-13更新
|
583次组卷
|
5卷引用:江苏省常州市金坛区2021-2022学年高一上学期期中数学试题
江苏省常州市金坛区2021-2022学年高一上学期期中数学试题2023版 北师大版(2019) 必修第一册 突围者 第二章 全章综合检测(已下线)5.4 函数的奇偶性(2)第二章 函数章末综合检测卷-2022-2023学年高一上学期数学北师大版(2019)必修第一册(已下线)专题3-6 抽象函数性质综合归类(1) - 【巅峰课堂】题型归纳与培优练
名校
解题方法
8 . 定义在
上的函数
满足
,
,且当
时,
.
(1)求证:
在
上是增函数;
(2)若
,解不等式
;
(3)比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349e9eef101d80afc99d1f893405b0fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427d892acbbf6db1da8cff8ad927ab22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4ed4485745f1d259a3953c242b9cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6060ac7fa3e4328073ca295cf2fc3f55.png)
(3)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d912c5d1e2408643e710eb5e8b4a4d49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b2e2042346a615e2a7cb95d0c57dcb.png)
您最近一年使用:0次
名校
解题方法
9 . 已知
,函数
的图象经过点
.
(1)求a的值;
(2)判断
的奇偶性并证明;
(3)判断
在区间
上的单调性并证明.(参考公式:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234b285a3ca8566e14c8f665f4f0c1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668d61a88b296ebd55a3b0bbc277539a.png)
(1)求a的值;
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f35c30f027c8d39805c829139fa915d.png)
您最近一年使用:0次
名校
10 . 已知函数
,
.
(1)求证:
为R上的偶函数;
(2)若函数
在R上只有一个零点,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4b13834f3ca8e3ec9e20bd6c02bd35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964a86e1c993a63710fd1c329e2dd37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-01-20更新
|
557次组卷
|
2卷引用:江苏省常州市教育学会2021-2022学年高一上学期学业水平监测数学试题