解题方法
1 . 已知函数
的定义域为
,值域为
,且对任意
、
,都有
,
.
(1)求
的值,并证明
为奇函数;
(2)若
时,
,且
,判断
的单调性(不要求证明),并利用判断结果解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3276b5e12396fc4753eb3f8254f9fa68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da9144b3862e0742ad23181df7833f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bcf5aa44b81b3ebbfcb08bd4d21379.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(2)若
![](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/3359f013aac2768a0c54cae1a95a158c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e7ff7777bcb4f8e80ebdc095cd9741.png)
您最近一年使用:0次
2017-10-17更新
|
507次组卷
|
2卷引用:山西省河津三中2018届高三一轮复习阶段性测评文数试题
2 . 已知函数
的定义域为
,值域为
,且对任意
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
,都有
,
.
(Ⅰ)求
的值,并证明
为奇函数;
(Ⅱ)若
时,
,且
,判断
的单调性(不要求证明),并利用判断结果解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160daec0ad9ccc242f3e259eb4d61ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b75d15ed45e8112211198215d04629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70129abba7b1f509a5f887a6695fed7.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2775ffdf695af2d263f0ea93ac5904.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e063be56fb2ae8bd907c4766f60401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa18fc03c117b1bb9fb6d4c08868e342.png)
您最近一年使用:0次
名校
解题方法
3 . 定义在R上的函数
,当
,且对任意
,有
.
(1)求证:对任意
,都有
;
(2)判断
在R上的单调性,并用定义证明;
(3)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84302e08e2e09d2d62548d35e6a40288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e885000d706e589a10515ff0d93cae55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db7387dec34f24cacb1cd95c433e8a4.png)
(1)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6d0da3cbcaa04a639eaac12c0e29d1.png)
您最近一年使用:0次
2017-02-08更新
|
1129次组卷
|
2卷引用:2016-2017学年浙江杭州西湖高级中学高一上学期期中数学试卷
名校
4 . 对于定义域为D的函数y=f(x),如果存在区间[m,n]
D,同时满足:
①f(x)在[m,n]内是单调函数;
②当定义域是[m,n]时,f(x)的值域也是[m,n].则称[m,n]是该函数的“和谐区间”.
(1)证明:[0,1]是函数y=f(x)=x2的一个“和谐区间”.
(2)求证:函数
不存在“和谐区间”.
(3)已知:函数
(a∈R,a≠0)有“和谐区间”[m,n],当a变化时,求出n﹣m的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637904facd16726fbfccb679e901e68a.png)
①f(x)在[m,n]内是单调函数;
②当定义域是[m,n]时,f(x)的值域也是[m,n].则称[m,n]是该函数的“和谐区间”.
(1)证明:[0,1]是函数y=f(x)=x2的一个“和谐区间”.
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3b0573a4ee2c68c86feda380291faf.png)
(3)已知:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a087c10b183ee28bc5fe1faa3289074.png)
您最近一年使用:0次
2016-12-04更新
|
1243次组卷
|
8卷引用:2016-2017学年安徽六安一中高一上国庆作业二数学试卷
解题方法
5 . 定义在R上的函数f(x)满足对任意的x,y∈R都有f(x+y)=f(x)+f(y),且当x>0时,f(x)>0.
(1)求证:f(x)为奇函数;
(2)判断f(x)的单调性并证明;
(3)解不等式:f[log2(x+
+6)]+f(-3)≤0.
(1)求证:f(x)为奇函数;
(2)判断f(x)的单调性并证明;
(3)解不等式:f[log2(x+
![](https://img.xkw.com/dksih/QBM/2015/12/3/1572340280983552/1572340286717952/STEM/01ab31e9eef64b32b6cb5138387e7b19.png)
您最近一年使用:0次
6 . 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)
11-12高一·河北邢台·阶段练习
解题方法
7 . 定义在
上的函数
,如果满足:对任意
,存在常数
,都有
成立,则称
是
上的有界函数,其中
称为函数
的上界.
(
)判断函数
,
是否是有界函数,请写出详细判断过程.
(
)试证明:设
,
,若
,
在
上分别以
,
为上界,求证:函数
在
上以
为上界.
(
)若函数
在
上是以
为上界的有界函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a1c02c533c60949a994212c90fbeda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adaa5b750211a0524fd66498aa0e8a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbb01a7f5e9861aa185c6c63fcd58c0.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a891d21bb2c7a11304beaab5054074.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfcc567b95a320abcb25509923cd001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae0f8520349250a31be6d58542ef2d9.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d866d4d7f9c7676657aa4ed4dfebd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
12-13高一上·四川巴中·期末
8 . 已知函数![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/7b4458986dc24c878b1bc6e464d0a8bd.png)
(Ⅰ)①判断函数的奇偶性,并加以证明;
②若
(-1,1),计算
;
(Ⅱ)若函数
在
上恒有零点,求实数m的取值范围;
(Ⅲ)若n为正整数,求证:
.
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/7b4458986dc24c878b1bc6e464d0a8bd.png)
(Ⅰ)①判断函数的奇偶性,并加以证明;
②若
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/689dd62d1194434b861d6519db247dad.png)
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/e014711e270c4c63bf082ebe16432dcf.png)
(Ⅱ)若函数
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/67ec7745a25e4fa0bdd28a138348d1bc.png)
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/b0b7086aa0ae4cf9a3855b2528f56bad.png)
(Ⅲ)若n为正整数,求证:
![](https://img.xkw.com/dksih/QBM/2012/2/2/1570710307332096/1570710312828928/STEM/d00c7b3cc477474ab2a54448b3fbb95c.png)
您最近一年使用:0次
9 . 设M是由满足下列条件的函数
构成的集合:“①方程
有实数根;②函数
的导数
满足
”.
(1)判断函数
是否是集合M中的元素,并说明理由;
(2)若集合M中的元素具有下面的性质:“若
的定义域为D,则对于任意
,都存在
,使得等式
成立”,试用这一性质证明:方程
只有一个实数根;
(3)设
是方程
的实数根,求证:对于
定义域中的任意的
,当
且
时,
.
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/ae69ca2dbf214361aaced19128f5b3ad.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/6021540f69a449d888b651a72c1479ef.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/ae69ca2dbf214361aaced19128f5b3ad.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/03232f0551f6467eac414c60d35586a1.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/9779437256ef4567a6622615f573e146.png)
(1)判断函数
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/abb75ec4ca244cb6acf77767c9e2801f.png)
(2)若集合M中的元素具有下面的性质:“若
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/ae69ca2dbf214361aaced19128f5b3ad.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/26bee806fbe340b69bb98cea2c4a27c1.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/9fe616bad37a46349490cadbc5d6eb0d.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/5f915debb4c64765aa8217365ab3ec4e.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/6021540f69a449d888b651a72c1479ef.png)
(3)设
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/666cf56f0d7547ef82a6ccd8c59ca96d.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/6021540f69a449d888b651a72c1479ef.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/ae69ca2dbf214361aaced19128f5b3ad.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/4407e7eea4b74ec884317d371fa5fd39.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/bf69921ad4954c8cb68344594560c1cb.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/0509a1f80c6e464e8b90705c0e053bb3.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/25d2084c3eb94f33935b3390721b5274.png)
您最近一年使用:0次
10 . 已知函数
.
(1)求证:
是偶函数;
(2)判断函数
在
和
上的单调性并用定义法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37ddf6c3e54ad634cf03a1be036242e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a8fc8767a57e739249aab76a79c896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65adaad9d9e240e0054e73a882a973e.png)
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