1 . (1)求证:函数
在区间
上是严格减函数;
(2)已知
且
,若
,求实数x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d77ff56ead5ca09cc22816f2f3b385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
(2)已知
![](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/a6c2cda3c64fabe845c6fc16e94d6c9f.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
(
且
)是定义域为
的奇 函数,且
.
(1)求
的值,并判断
的单调性(不要求证明);
(2)是否存在实数
,使函数
在
上的最大值为0?如果存在,求出实数
所有的值;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a0efb23a59a82e6dd3252778f04ee.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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a98186dcca4e3093a3e910b705b087.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1533fdab20809be5fa471a8d34e9e456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd9c440eb35d3edc3516a8ac4358e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-12-01更新
|
462次组卷
|
4卷引用:大题能力提升考前必做30题-2020-2021学年高一数学期末考试高分直通车(沪教版2020,必修一)
(已下线)大题能力提升考前必做30题-2020-2021学年高一数学期末考试高分直通车(沪教版2020,必修一)湖北省荆州中学2020-2021学年高一上学期期中数学试题(已下线)第四单元 (综合培优)指数函数与对数函数 B卷-【双基双测】2021-2022学年高一数学同步单元AB卷(人教A版2019必修第一册)(已下线)第四单元 (基础过关)指数函数与对数函数 A卷-【双基双测】2021-2022学年高一数学同步单元AB卷(人教A版2019必修第一册)
解题方法
3 . 求证:函数
在区间
上是增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac4654dd6b6dca4b27aa371080e2df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
您最近一年使用:0次
名校
4 . 设
,
是函数
的图像上任意两点,点
满足
.
(1)若
,求证:
为定值;
(2)若
,且
,求
的取值范围,并比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05193d9096bd9da9230acc14228aa4e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4920bf4db93b18d4ecfdc05e310dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21de984f69bcc0bec2c5580d2dc6b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/961e120bfd1da71d31f9dc204c0e851c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5f702b56a32a3b31c8eee63fbcf8be.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e099a6abe3e9566b2ad385906e323fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a86d65aab881fdd06a05ce47d09c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e7dc5d31b6378f40d36b132857e1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
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2020-05-21更新
|
291次组卷
|
3卷引用:2020届上海市黄浦区高三二模(阶段性调研)数学试题
5 . 已知函数
,其中
.
(1)当
时,求证:函数
是偶函数;
(2)已知
,函数
的反函数为
,若函数
在区间
上的最小值为
,求函数
在区间
上的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46de5284a8d6ccf8abef40c9003613b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9f7295ceeae71c9db819fa21b4d325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a67558257699bd7125c174190b3d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
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2020-02-09更新
|
319次组卷
|
2卷引用:2016届上海市杨浦区高三4月质量调研(二模)(文)数学试题
6 . 已知定义在实数集
上的偶函数
和奇函数
满足
.
(1)求
与
的解析式;
(2)求证:
在区间
上单调递增;并求
在区间
的反函数;
(3)设
(其中
为常数),若
对于
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41ae210dd892fc5428a51dd409aa69d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b029e85e686623cdef977b2cb1f207a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b029e85e686623cdef977b2cb1f207a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4db4036616944674cc36bb1388a2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10dc986f44a2f80e9b8d192eb3521398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-02-04更新
|
649次组卷
|
2卷引用:2016届上海市静安区高考一模(文科)数学试题
名校
7 . 已知函数
.
(1)求证:函数
在
内单调递增;
(2)记
为函数
的反函数.若关于
的方程
在
上有解,求
的取值范围;
(3)若
对于
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7550c4398d252c62fb2c7ea6dc2b3ff0.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ff4a1f5d3ad9d7668fe555e70b774c.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a2a1822ac7392b61b2c0fffc1fbc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8944bd9fdb023bdda9b5f8b73e43c21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b374fed1d05423919f0663ab2d0d8f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2020-02-01更新
|
243次组卷
|
2卷引用:上海市上海师大附中2016届高三上学期期中(文科)数学试题
名校
8 . (1)已知
,求证:
.
(2)已知
,求证:
在定义域内是单调递减函数;
(3)在(2)的条件下,求集合
的子集个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8babf018f42b32990f65768ed81ef5.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ea5e39c4f2025dbd80d8629c6b71e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)在(2)的条件下,求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3fd56c0a0ba232750157d2241284959.png)
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2020-01-16更新
|
235次组卷
|
5卷引用:上海市七宝中学2017-2018学年高二上学期开学考试数学试题
9 . 已知非空集合
是由一些函数组成,满足如下性质:①对任意
,
均存在反函数
,且
;②对任意
,方程
均有解;③对任意
、
,若函数
为定义在
上的一次函数,则
.
(1)若
,
,均在集合
中,求证:函数
;
(2)若函数
(
)在集合
中,求实数
的取值范围;
(3)若集合
中的函数均为定义在
上的一次函数,求证:存在一个实数
,使得对一切
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5f5f81ea1a02b88ff8491fcf4937db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a2a1822ac7392b61b2c0fffc1fbc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7de4de1315f460681d9da70dd8fc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5f5f81ea1a02b88ff8491fcf4937db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbec485ab7b15f1e09f163fe990577c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd1f807dd5b1507c823ad8c1db55a6c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c8726575585ccd6e00c02033825374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e62e7482ee75b0768111a4df5f0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10c7b4247b574fc4b71d6e02ebf2d20.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e5552d315d2ea9b01d112dca830754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5f5f81ea1a02b88ff8491fcf4937db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bc955d158efde0bdd62d14a60a65e3.png)
您最近一年使用:0次
2020-01-16更新
|
774次组卷
|
3卷引用:2016届上海市杨浦区高三5月模拟(三模)(理)数学试题
名校
10 . 已知非空集合
是由一些函数组成,同时满足以下性质:
①对任意
,
均存在反函数
,且
;
②对任意
,方程
均有解;
③对任意
,若函数
为定义在
上的一次函数,则
;
(1)若
,
均在集合
中,求证:函数
;
(2)若函数
在集合
中,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
①对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcd04b625189228b6d697edf095f7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d95e3998987a7dda4fc7dfb3f2d57d.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcd04b625189228b6d697edf095f7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
③对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87db4b7888b08d6f5c27cd745b66e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2787142cbc51f5bcbffda80849ce17b4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679da8a975f3a340f456d205b9da9a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2197038d74821f5151b6d513048a5a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff12d01f4c4c6983bac86c992b2ae87.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaa82beb00bb0cfc14fd36468b89d69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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