解题方法
1 . 已知函数
.
(1)用单调性定义证明:
在
上单调递增;
(2)若函数
有3个零点
,满足
,且
.
①求证:
;
②求
的值(
表示不超过
的最大整数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247d7790d83be16bc74aa5e5d12dd63.png)
(1)用单调性定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f8994d83bf4a688c0ab897a5a40fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1cc5cfec94bc5686b41b043acdc8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d995c5d2e1e0305d805032e18997986a.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28cbe8f17c4472d8663f9ccbe3b98f6.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59077d1948911b13d68a572eadbca3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
解题方法
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad292a5e3f68651844e4207b9b594bf.png)
(1)直接写出函数
的零点和不等式
的解集;
(2)直接写出函数
的定义域和值域;
(3)求证:函数
的图象关于点
中心对称;
(4)用单调性定义证明:函数
在区间
上是减函数;
(5)设
,直接写出它的反函数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad292a5e3f68651844e4207b9b594bf.png)
(1)直接写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)直接写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b334e2eaa7e8fb79cef8208b56ee4f5.png)
(4)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/3e10140ab3cdc13d710a65b2287c892b.png)
(5)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e313b39064db7bfb103e6215440b19e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc58675aca9c02251a17d4fca67ea5dd.png)
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名校
解题方法
3 . 已知二次函数
满足
.
(1)求
,
的值;
(2)求证:
的图像关于直线
对称;
(3)用单调性定义证明:函数
在区间
上是增函数;
(4)若函数
是奇函数,当
时,
.
(i)直接写出
的单调递减区间为_________;
(ii)求出
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab93efd42a3054040ccff8adf697c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3749d9ddfb2908ac0ee444743fe72afd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
(3)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/189b2da6c420bf8f8900002d14f65f72.png)
(4)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d1a94ea3c278c2197572cc1b7725b1.png)
(i)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(ii)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
解题方法
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeccfff03711ca585eb358459dc68107.png)
(1)求证:用单调性定义证明函数
是
上的严格减函数;
(2)已知“函数
的图像关于点
对称”的充要条件是“
对于定义域内任何
恒成立”.试用此结论判断函数
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/eeccfff03711ca585eb358459dc68107.png)
(1)求证: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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)已知“函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8319f56cfb802b0e049b4765b5ec79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4003115706a191f2d4415119e73ddaa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9902484b765fe634029040cc5dae6cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8ef8cdf661a9557e490588ef45dcfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
5 . 设函数
的定义域为
.若存在常数
,
,使得对于任意
,
成立,则称函数
具有性质
.
(1)判断函数
和
具有性质
?(结论不要求证明)
(2)若函数
具有性质
,且其对应的
,
.已知当
时,
,求函数
在区间
上的最大值;
(3)若函数
具有性质
,且直线
为其图像的一条对称轴,证明:
为周期函数.
![](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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809ea2eff71a0de3db640313ad25b7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404d068b60dd901194f1684d023212ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8073fa685bc10cf01a0128220feac940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e661ad31aa4c6d8684923cf904bf1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d0588454ec8b64bf86578fb90b39e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55351494cd96fed31976fdc5d9c7292.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
2021-08-01更新
|
588次组卷
|
3卷引用:北京市西城区2020-2021学年高一下学期期末数学试题
解题方法
6 . 已知定理:“若a,b为常数,
满足
,则函数
的图象关于点
中心对称”,设函数
,定义域为A.
(1)试证明
的图象关于点
成中心对称;
(2)当
时,求证:
.
(3)对于给定的
,设计构造过程:
.如果
,构造过程将继续下去;如果
,构造过程将停止.若对任意
,构造过程可以无限进行下去,求a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848df4eb73fcb06c262064e1049db419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c3d3eca937b665f6a6484d68ba72e8.png)
(1)试证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d9012ae3226e6f1d338f879c180ce63.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d56cfb272d729b7b1b9510d246747f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7368d91031473c697c9cd43cda57380.png)
(3)对于给定的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa273c6bf06db59f93c900e6bf8eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dbf2c2f1750bef15d8c2c129f495a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60a7337d2eb93fc80a7d2c5da7043c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedd176503d53573b0d7ceb03d933700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa273c6bf06db59f93c900e6bf8eb55.png)
您最近一年使用:0次
名校
7 . 已知函数
,而函数
的图象与
的图象关于
轴对称.
(1)直接写出函数
的解析式;
(2)令
.判断函数
的奇偶性并证明;
(3)求证:函数
是定义域上的增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e7bf52653b3f47440082de68cb050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2316563595e29fd4279845ab8afc5ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)直接写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2316563595e29fd4279845ab8afc5ba2.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2c2b6a8f27fd598d1efccdfe1a74c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2c2b6a8f27fd598d1efccdfe1a74c0.png)
您最近一年使用:0次
8 . 现定义:设
是非零实常数,若对于任意的
,都有
,则称函数
为“关于的
偶型函数”
(1)请以三角函数为例,写出一个“关于2的偶型函数”的解析式,并给予证明
(2)设定义域为的“关于的
偶型函数”在区间
上单调递增,求证在区间
上单调递减
(3)设定义域为
的“关于
的偶型函数”
是奇函数,若
,请猜测
的值,并用数学归纳法证明你的结论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55550151ed0b0264fce45814acfc725a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)请以三角函数为例,写出一个“关于2的偶型函数”的解析式,并给予证明
(2)设定义域为的“关于的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f0b8dcc8ea36ef8093122d4efbedc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a8f80511de15d3dfb871ca2f400424.png)
(3)设定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5cf9c12181dd8683944b2b30bf8e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
您最近一年使用:0次
2019-12-31更新
|
333次组卷
|
5卷引用:上海市静安区2019-2020学年高三上学期期末数学试题
上海市静安区2019-2020学年高三上学期期末数学试题2020届上海市静安区高三一模(期末)数学试题(已下线)第四章++数列1(基础过关)-2020-2021学年高二数学单元测试定心卷(人教A版2019选择性必修第二册)(已下线)热点02 函数及其性质-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)第二章 推理与证明(基础过关)-2020-2021学年高二数学单元测试定心卷(人教版选修2-2)
9 . 已知定理:“若
为常数,
满足
,则函数
的图象关于点
中心对称”.设函数
,定义域为A.
(1)试证明
的图象关于点
成中心对称;
(2)当
时,求证:
;
(3)对于给定的
,设计构造过程:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29906a2db5808848d60e4370768c3a4c.png)
,…,
.如果
,构造过程将继续下去;如果
,构造过程将停止.若对任意
,构造过程可以无限进行下去,求a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd2972db22f90c3df0a20ac1399e0c18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e74626057ec436bfec1a74056f179.png)
(1)试证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db39aac652d63d0ea8d692ab18c34a3c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062e0b17c2777b51c5c61d6696f84a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2866e54c043bc21996b058bb87bbfb7.png)
(3)对于给定的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c9201f95704ba1b11eafb60817afb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29906a2db5808848d60e4370768c3a4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8401b72447ea9491010079eca6e967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0cf06beb7cfde2c2ce4796bfe6d7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51bb5492f7c7f15ae1d68398a539e506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd5b8ce755692bb39da80789e55ad65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c9201f95704ba1b11eafb60817afb0.png)
您最近一年使用:0次
2016-12-03更新
|
702次组卷
|
3卷引用:2015届江苏省如东高中高三上学期第9周周练理科数学试卷
2015届江苏省如东高中高三上学期第9周周练理科数学试卷人教A版(2019) 必修第一册 突围者 第三章 综合拓展(已下线)第五章 函数概念与性质(选拔卷)-【单元测试】2021-2022学年高一数学尖子生选拔卷(苏教版2019必修第一册)
解题方法
10 . 已知函数
,等差数列
的前
项和为
,记
.
(1)求证:
的图象关于点
中心对称;
(2)若
,
,
是某三角形的三个内角,求
的取值范围;
(3)若
,求证:
.反之是否成立?并请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47665ff46fcf594d4151c3a89707257f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7830b11dc2634eb661673a04287ddc6.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ebbb2eab12b76127cc87304c212cdd6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155c5f3a5c55e0c95191c5a893f63062.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca95ba448d33b5e82aa1a3591dc0adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4615a158e82ab5ff2c3a84f13d1ccda.png)
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