1 . 设集合
.定义:和集合
,积集合
,分别用
表示集合
中元素的个数.
(1)若
,求集合
;
(2)若
,求
的所有可能的值组成的集合;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59889190d638327c0b0b0cc162d41221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f706563c8dc02e70264ce4211a89c709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaec9915cb9f6c01cb87a6c7b0d121b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c376afabc2928dd4299dca55d5bfc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9e6ad1166c7625e63b80e75b2fb1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2734b136f9961df15bb51c31e29e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8f054b30b493c4ce1deecff3468c08.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d197338ab810f6c9d31a2b67e5f352ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef01842529a2a0028f17f35b6281e1a.png)
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2 . 已知函数
和
的定义域分别为
和
,若对任意
,恰好存在n个不同的实数
,
,…,
,使得
(其中
,2,…,n,
),则称
为
的“n重覆盖函数”.
(1)判断
(
)是否为
(
)的“n重覆盖函数”,如果是,求出n的值;如果不是,说明理由;
(2)若
为
的“2重覆盖函数”,求实数a的取值范围;
(3)函数
表示不超过x的最大整数,如
,
,
,若
,
为
,
的“2024重覆盖函数”,求正实数a的取值范围.
![](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/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eddf991be37d25d033f78bd3511809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc40290feeafceca34cbdab068dcd769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44a5aed663a9b61ef7355b38c77d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986cf0c6c92f8a0e0370b50d5606d483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365114c53aa12abda1004c8e4cb4ca0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1b4a895643b6b3cfddbe5d4a1157b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8160ade472b89421f8009fd0cd3926a3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f246e5b05b68bb9fdeb12a319aa7136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa88c20e58953bba4ed04d3ce419df95.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe1e778c9e668594c42b77459328c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3420606c96b68fb884c839923fd20a25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf813e9500eebd474511b865b876ea4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0c6435833958c7987934c3367d48b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50af11c345056215054f7cfe679939da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5877b36b0def7389b8fb66e8491644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
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3 . 已知函数
.若
,不等式
恒成立,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b919a59954cf503f515e45573deba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9f109b7ce6ec37e69d54ec70643c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab0b80b5c44b0273a75e752ad0fd7f3.png)
(1)若函数
的值域为
,求实数
的取值范围;
(2)若不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab0b80b5c44b0273a75e752ad0fd7f3.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074a1239cc02c3d8a9530f40c2c42679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0098955a331f9f7550fabd63c818a9a.png)
(1)当
是奇函数时,解决以下两个问题:
①求k的值;
②若关于x的不等式
对任意
恒成立,求实数m的取值范围;
(2)当
是偶函数时,设
,那么当n为何值时,函数
有零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0098955a331f9f7550fabd63c818a9a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①求k的值;
②若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd47cc4fc009bda52a56b0a74db3b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3368388525e30cb7179909b03184eb.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43049e7a019652c5c85b01bc0011032f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ca992b5b470255a859aa8aa24cd785.png)
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|
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6 . 已知函数
为常数).函数
定义如下:对每个给定的实数
.
(1)若
,求
在
上的最大值;
(2)若
且
,求函数
在区间
上的单调增区间的长度之和.(闭区间
的长度定义为
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095878335d1f0c342afc4a2a300edfe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f842876e8f512903598574fa62e86e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e1c681b27df538bd4742f6cd8298ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575002003f89bc8309a2c7f206761794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa21416f901e005780f383fb029e86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede949a2fe7bf9f1f98f5457d408b41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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2卷引用:浙江省宁波市镇海中学2023-2024学年高一上学期11月期中考试数学试题
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解题方法
7 . 已知函数
(
、
),
.
(1)设
的解集为A,
解集为
,若
,求实数
的取值范围;
(2)已知函数
的图象关于点
对称,当
时,
,若对任意的
,总存在
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63aaa178677e179fd17fb87877ccb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c174a494bd5543e276f7813df78197.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df128531a4c909d0d60b4f472da55fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d02e5de0c92487382f4b98376e9740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0cfceb10b2ff10bf43b56485d67b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fa5cb4b09c5042827e90f5b2071665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0391e39aaeb4e3cc883b0439d7f69d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b56a0bc723618e7cdac994882c807bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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解题方法
8 . 已知函数
.
(1)当
时,解方程
;
(2)若对任意的
都有
恒成立,试求m的取值范围;
(3)用min{m,n}表示m,n中的最小者,设函数
,讨论关于x的方程
的实数解的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d900172f57cb0c0cbefb40c8bdf978.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8bfb563f79688d136e0cb958b5153c.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05da3f440c24f995eeaaa9a59bfdd92b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59554ee8b854e90a459d27524b5003df.png)
(3)用min{m,n}表示m,n中的最小者,设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adc05d41c7f7cf508d6afea3cc0912a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42e9e85ab98860058623847c3eb20b3.png)
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2023-03-22更新
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1034次组卷
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解题方法
9 . 已知函数
的定义域为
为奇函数,
为偶函数,当
时,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2becb8c04d632ce418ee8a467967f1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d0e9cd42a043be4c6e552c6cf4cbdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0810d505a46fc0c3a11eee665469646e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5ff6072bb799712801e9375d433783.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.方程![]() |
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解题方法
10 . 已知实数
,
满足
,则下列关系式可能正确的是( )
![](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/b5e2c8e3a7e759bf13c31e3826886100.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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2023-02-18更新
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3卷引用:浙江省宁波市2022-2023学年高一上学期期末数学试题
浙江省宁波市2022-2023学年高一上学期期末数学试题吉林省吉林市第一中学2023-2024学年高一上学期9月月考数学试题(创新班)(已下线)第四章 指数函数与对数函数(压轴题专练)-速记·巧练(人教A版2019必修第一册)