名校
解题方法
1 . 设函数
的定义域为D,对于区间
,当且仅当函数
满足以下①②两个性质中的任意一个时,则称区间
是
的一个“美好区间”.
性质①:对于任意
,都有
;性质②:对于任意
,都有
.
(1)已知
,
.分别判断区间
和区间
是否为函数
的“美好区间”,并说明理由;
(2)已知
且
,若区间
是函数
的一个“美好区间”,求实数
的取值范围;
(3)已知函数
的定义域为
,其图像是一条连续不断的曲线,且对于任意
,都有
.求证:函数
存在“美好区间”,且存在
,使得
不属于函数
的任意一个“美好区间”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b7f3c56708bc693a0ce74643be38cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
性质①:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b359345c5afa1739bf5ebf8982e1d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198025cc2e6afede12c13375b71e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b359345c5afa1739bf5ebf8982e1d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab98f168e7e388981a83c792bef034de.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4078f129da5a6cb569345de01c4d019c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2cc4cd1e8bcb4b75b6e799156736e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9099a75c433e97bbe05052a00110571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bed897a25d7f5d6d4693e3076023745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257b5cac000fa7c846215d986d6aa90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a173c108f4d3a4e8b641724d966d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070054c0b4182ab7399ed56925844e93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
您最近一年使用:0次
7日内更新
|
140次组卷
|
3卷引用:上海市 位育中学2023-2024学年高三下学期三模数学试题
名校
解题方法
2 . 已知函数
,①若函数
有最大值,并将其记为
,则a的最大值为
,
的最小值为
;②若函数
有零点,并将零点个数记为
,则函数
为偶函数( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e1b7dba1dfcdcc45a6e2c8c9e37175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e027a112d5a4aaaa510d38f3bcfd0311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e027a112d5a4aaaa510d38f3bcfd0311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619feadea70fc427acafbb7b8e10c47b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812e6b48ae696cc64924b993176caf57.png)
A.①成立②成立 | B.①成立②不成立 |
C.①不成立②成立 | D.①不成立②不成立 |
您最近一年使用:0次
名校
3 . 已知定义在
上的函数
,若存在实数
,
,
使得
对任意的实数
恒成立,则称函数
为“
函数”;
(1)已知
,判断它是否为“
函数”;
(2)若函数
是“
函数”,当
,
,求
在
上的解.
(3)证明函数
为“
函数”并求所有符合条件的
、
、
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d637d748a2b196af6d91703881ae1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67758380edd3796902534cf0e52cb6a1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9697e701323f29c2b8fb4b69fdec2a50.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901a683d7456f2b2135bccb41e70e33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad324be3bebd9c8051c5f502df2b536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51870c1132971c292e4498255210546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4947f55ebd9b5438e46cb120d51be615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966055559e213bce8e92ef59ba03d2d4.png)
(3)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa79143526cf263a8fff8030446efa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67758380edd3796902534cf0e52cb6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
您最近一年使用:0次
2024高三·上海·专题练习
解题方法
4 . 设函数
在
上有定义,实数
,
满足
.若
在区间
上不存在最小值,则称
在区间
上具有性质
.
(1)若函数
,且
在区间
上具有性质
时,求常数
的取值范围;
(2)已知
,且当
时,
,判别
在区间
上是否具有性质
,并说明理由;
(3)若对于
的任意实数
和
;函数
在区间
上具有性质
,且对于任意
,当
时,有:
,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1accdaf7d28bf884e8a044a8960190ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152e7be0c0054be3a8d537ef39d35da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152e7be0c0054be3a8d537ef39d35da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9635084c172726da8e140d6c9044a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337a23f9bf790be6e03b88fb2d03f18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630188a3505f47c8d2098c92475cf191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a31f7a8c150b3f4e720db0401fd5fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffbd6d46c75b7454cc1259ed8d818ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992d70084c8512958a36ac591e74f617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)若对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1accdaf7d28bf884e8a044a8960190ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152e7be0c0054be3a8d537ef39d35da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b66875df124e8b7255feaea8e0c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea1ba78ae2c541ac99bd30802e0e1cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b67cac8abe9566def881056297caf0d.png)
您最近一年使用:0次
名校
解题方法
5 . 已知定义在
上的函数
,集合
.
(1)若
,是否存在实数k,使得
,如果存在,求k;如果不存在,说明理由;
(2)若
,且当
时,
,求函数
在
的函数解析式;
(3)若
,是否存在一次函数
,使
,其中
,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279133c0f4a56f184329d132ad6357c8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4046c9f58f541732bd4d90b7719ba35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fa4434ffb809ce49a20db2aee573e4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89d2c6a4bf4dd5296ec48b3cb961db00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbb01a7f5e9861aa185c6c63fcd58c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19a14a9712f66204093b9dda61927b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f103a01fa039701e147e4b7e9353e999.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae92289c9645da9e330fee632aee99db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3062b19939118118a668ba074d14bbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b94fda0a88d994de1f73d1e37dc73ab.png)
您最近一年使用:0次
名校
解题方法
6 . 德国数学家狄利克雷在数学领域成就显著,以其命名函数
,该函数被称为狄利克雷函数,关于狄利克雷函数有如下四个命题:
①
;
②对于任意的实数
,均有
;
③
为偶函数;
④存在无数个实数
,使得
;
⑤若存在三个点
、
、
,使得
为等边三角形,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6142328578de5c2d0353727ab4a9396d.png)
其中真命题的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1bd86b77d0c78616128257cdd2fd3f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7debbe276b0c456c466746619311d4d.png)
②对于任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a61621c4d089181036524ae9833ebb.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac13cefe2757e8f741bd0e8ded954bcf.png)
④存在无数个实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c075d8f5fd064808a54e9a9b98932f.png)
⑤若存在三个点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd9e756e1da0ae9beed0c9c117b74178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee173145668f082751c6e9d629e8cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836e5321ec22c9840a195bc146861cee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6142328578de5c2d0353727ab4a9396d.png)
其中真命题的序号为( )
A.①③④⑤ | B.①③④ | C.①②④⑤ | D.①②④ |
您最近一年使用:0次
名校
解题方法
7 . 已知
记函数
的最大值为
,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22468a3e2b06b65e0f177c14f38f265b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
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名校
8 . 已知函数
的表达式为
,若方程
有四个不相等的实根
,且
,则
取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664d5a568352ae5c7bb21549055ecd7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e3397839f4b65912c2f0cfe7f05eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd42c34b2f926f4600e8622b961e3c92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4077511e2a6cd8caff76581a94b6fe.png)
您最近一年使用:0次
2024-01-15更新
|
219次组卷
|
2卷引用:上海市松江区2023-2024学年高一上学期期末质量监控数学试卷
9 . (1)
是定义在正整数集上的函数,并且满足
①当
为正整数时,
;
②当
为非负整数时,
.
求
的值.
(2)函数
定义在有序正整数对的集合上,且满足下列性质:
①
;②
;③
.
求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f6c12705300de947fc04865b2747cd9.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6360d35614281c3a6b08179ef77cc4c.png)
求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495955d39b954d26852f3f58c9df0a03.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e21e386e8449fe122efe8789ab77e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217758c83175763d7d3c306d12c22176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e67dd773c99cf71254097f7a838ae7a0.png)
求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30547752a04f8877c99a1084c6e145e3.png)
您最近一年使用:0次
解题方法
10 . 设函数
,其中
,其中
,若函数
的图象与直线
有4个交点,则实数b满足的条件是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b19a4e4a40d304dbdad592278a0511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d300a3a6d3270bccac16b34fd7a3cb5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911d041b94b357e0b2c9c6b28a4bec2e.png)
您最近一年使用:0次