名校
解题方法
1 . 设实数a、b
R,
.
(1)解不等式:
;
(2)若存在
,使得
,
,求
的值;
(3)设常数
,若
,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02d44492b51b0e08208fdc0d1707025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ee5110dc97139c96c04eae63749ffb.png)
(1)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaefd950e97a1c2b16bd479d0888bf5.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5223ece2f8f76850c49e2505304532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0987f16ec008febdd80ef3edcca6b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8331e543dfd7eb846138bf3933823f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
(3)设常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f04d5d5f4ed51b04c05ed5313ede65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e588668be1d899d1072b63f345f2cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e420a6bb4a3243d4902a26193a4cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4628491e3b01e3b849b329b4ec78bb3.png)
您最近一年使用:0次
2022-05-05更新
|
1315次组卷
|
3卷引用:第03讲 函数及其性质-2
名校
解题方法
2 . 已知函数
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c85467b0027305f2d3757b0ba5bf8b.png)
(1)若
,且
,试比较
与
的大小关系,并说明理由;
(2)若
,且
,证明:
(i)
;
(ii)
.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1060c34e676f9e4048f396023fa6a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87dad80ff155f615b17fbe8bf4db00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c85467b0027305f2d3757b0ba5bf8b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477401fbd54f365121b648e4d8fcf38b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f13c49cbcdca5ed2e81d229819357b9.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6ecd08de6b156b5fa2bda453c855f3.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe64030d6e08f7607b7e3d9a724a79c9.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9e0f63cd71701bdf260b1510c72ee8f.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
的定义域是D,若对于任意的
,
,当
时,都有
,则称函数
在D上为不减函数.现有定义在
上的函数
满足下述条件:
①对于
,总有
,且
,
;
②对于
,若
,则
.
试证明下列结论:
(1)对于
,若
,则
;
(2)a)
在
上为不减函数;
b)对
,都有
;
(3)当
时,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61c8d37c767ba727cc7f5f7e00a7d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb7af9e416682c9be1ff154ec3fbfdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c24244b1fdbf1455087c2ebf41c8b.png)
②对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0232209f5de09f72b997e0099b9de5f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7563ceaa2d4ae02f31d47b53708edc75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff755b55a86b26a7f3e7def591b5b315.png)
试证明下列结论:
(1)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3367bd41ff428d7a608511cfb1f3cb11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa468658500142da664ca688d4d4d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d096dd04098cafabf4211054353feec8.png)
(2)a)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
b)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e511095b9802e0e54c3bcac8be160e58.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6101294ff728fdef676a5786590908.png)
您最近一年使用:0次
名校
解题方法
4 . 定义
为双曲正弦函数,
为双曲余弦函数,它们是一类与三角函数类似的函数.
(1)试判断双曲正弦函数
的单调性,并用定义证明;
(2)①类比同角三角函数的平方关系,试写出
与
的关系式,并给予证明;
②对
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e183cfec7ad0c15ba454415017e3ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3442020c24433f0e30b455d3e2bd0e3.png)
(1)试判断双曲正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ae841e173b7700db59a369202dcbcf.png)
(2)①类比同角三角函数的平方关系,试写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ae841e173b7700db59a369202dcbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499a131f534409ee96f17e1d9f44b9e.png)
②对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c08d4d681c6e84e695b2a467dde8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77474ddd5262fcbf0877981ce802adb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-03-17更新
|
475次组卷
|
2卷引用:专题03E函数解答题
解题方法
5 . 给定集合
,
为定义在D上的函数,当
时,
,且对任意
,都有___________ .
从条件①、条件②、条件③这三个条件中选择一个作为已知,补充在横线处,使
存在且唯一确定.
条件①:
;
条件②:
;
条件③:
.
解答下列问题:
(1)写出
和
的值;
(2)写出
在
上的单调区间;
(3)设
,写出
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb878f1866c06162fab3dae6aa76d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3854657132149e031bf23eed96479cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
从条件①、条件②、条件③这三个条件中选择一个作为已知,补充在横线处,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fa1cb589c89ba5d858717ab749d0ed.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be2cdbc2173fc2efcec1085e6ef9ace.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8352dff123dd14331a3d6c74514c290a.png)
解答下列问题:
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b530377e3fe56b7988935dd73d9dccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e84fd2b0f03af2e72c838484e69e06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
您最近一年使用:0次
2022-03-11更新
|
1100次组卷
|
4卷引用:重难点01七种零点问题-2
2022·上海·模拟预测
6 . 已知函数
,甲变化:
;乙变化:
,
.
(1)若
,
,
经甲变化得到
,求方程
的解;
(2)若
,
经乙变化得到
,求不等式
的解集;
(3)若
在
上单调递增,将
先进行甲变化得到
,再将
进行乙变化得到
;将
先进行乙变化得到
,再将
进行甲变化得到
,若对任意
,总存在
成立,求证:
在R上单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e746284f8292034744ef19606f34ba0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7da1ccb2c68857801d3684316685994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697a2a61d367fe01830b6b5995a2c38d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3deb8eb89eb6be966c64d81acb292b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9414348d57c7fc77dcfa8f0744cb0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a4df880ff8c0322708ca3048aa665c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a4df880ff8c0322708ca3048aa665c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef23cf7d8c1b7e52a15e052768cd055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733b1f3ace6bd767fe4a26dc8098b8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733b1f3ace6bd767fe4a26dc8098b8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf729dc97c117b83cfa0769e02e3ce1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e15191afd613e5d8215bfa73ac86ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
解题方法
7 . 已知函数
的定义域为
,若存在常数
和
,对任意的
,都有
成立,则称函数
为“拟线性函数”,其中数组
称为函数
的拟合系数.
(1)数组
是否是函数
的拟合系数?
(2)判断函数
是否是“拟线性函数”,并说明理由;
(3)若奇函数
在区间
上单调递增,且
的图像关于点
成中心对称(其中
为常数),证明:
是“拟线性函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9eb0abfebb7bb39204e9aa051aa7f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85899a6f573914e34170ea6b2e6b27cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109d7264547e05af38ef2f36ec31f6d4.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188074ba24ae37b38cc0c614a2274d88.png)
(3)若奇函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad7349dcd23527bce8da3e344459659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
名校
8 . 设
的定义域是
,在区间
上是严格减函数;且对任意
,
,若
,则
.
(1)求证:函数
是一个偶函数;
(2)求证:对于任意的
,
.
(3)若
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff565afbddafe8625ef376d7eb3fa649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc2435121b2b68da22ba4662e5734c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333cf846facfab1283527ebe48961a95.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)求证:对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5967cc62862986840af4dd29df4bcc41.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f8b235e47a99a065a102c259b81db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3059047431efe07f36b3fb319f709a78.png)
您最近一年使用:0次
2021-11-26更新
|
1219次组卷
|
5卷引用:专题03 函数的概念与性质(练习)-2
(已下线)专题03 函数的概念与性质(练习)-2(已下线)上海高一上学期期中【压轴42题专练】(2)(已下线)专题3-6 抽象函数性质综合归类(2) - 【巅峰课堂】题型归纳与培优练上海市复旦大学附属中学2021-2022学年高一上学期期中数学试题重庆市南开中学2022-2023学年高一上学期12月月考数学试题
9 . 设
.
(1)求证:
在区间
和
上均为单调递减函数;
(2)问:
在区间
上是否为单调递减函数?为什么?
(3)推广至一般结论,讨论函数
(k为非零常数)的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f67ebe3b975f0b846a38a76eff0dbf.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe12fb284fc8e2502c9043be594c852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b36a0866ec5fbb94e6cf4d61579e0b.png)
(2)问:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1097c60bae6a91a5d3c1c6d4a60490.png)
(3)推广至一般结论,讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e29a631e052d3a682b025e512f0618.png)
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