1 . 已知定义在实数集
上的偶函数
和奇函数
满足
.
(1)求
与
的解析式;
(2)若定义在实数集
上的以2为最小正周期的周期函数
,当
时,
,试求
在闭区间
上的表达式,并证明
在闭区间
上单调递减;
(3)设
(其中
为常数),若
对于
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e9a48415eb87144dbd4630320da811.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
(2)若定义在实数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387570acb93efd8b7079bcda50743123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6343069217cd6d8dd32446da428dae46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72889ec56010bdbf9ed3aa91b3f97ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387570acb93efd8b7079bcda50743123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9555abad284dcdc5cfa290b047f77c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387570acb93efd8b7079bcda50743123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9555abad284dcdc5cfa290b047f77c3d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d4127926f1fa10d8ecfb4ed4b29415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6ee1f6c8d675a8933ebdde6191021c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a349161b52f9493112280309454cd9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-02-04更新
|
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2卷引用:2016届上海市静安区高考一模(理科)数学试题
2 . 对于定义在
上的函数
,若存在正常数
,使得
对一切
均成立,则称
是“控制增长函数”,在以下四个函数中①
②
,③
,④
是“控制增长函数”的有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cdb3c7e299e1b88199a7e3ca97ccde2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c956017c5ef0082731ab8ba67d19a760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbef77750d09f296107db0bfd9ae3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499aea26f78e0901eed6576f789d8747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9a1e4839e28aff4eeb31ba18c959bf.png)
A.①② | B.③④ | C.②③④ | D.①②④ |
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3 . 若函数
和它的反函数的图象与函数
的图象分别交于点A、B,若
,则a约等于________ (精确到0.1).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5e585060f4b5ae83158cd10345f14d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699fc9b7e879af4866aaa07848dfb423.png)
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4 . 对于函数
定义
已知偶函数
的定义域为
当
且
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a2517f0164e720ac65d4712255a19.png)
(1)求
并求出函数
的解析式;
(2)若存在实数
使得函数
在
上的值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a28166da2b2a5e0717de00fd5b091b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b89b3eef7de7a81892b5e360a175194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6466fc908c4968e38ad7ad9692320051.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b366bd12b731cfa3dda3a8b86d10f194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a0b7b0df4f3429acbe1e9ce652741c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a2517f0164e720ac65d4712255a19.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3680b70df17f7751ff54f542c41132c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cad6d62f380f8eab9bdb542fd821f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa457202281cca305e60eb4444aca3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a2c65c1d0c94d07c625701f87015db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b68034e76dfd3a44fed80314ad53c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2卷引用:2016届上海市虹口区高考一模数学试题
5 . 给出下列四个命题:(1)函数
的反函数为
;(2)函数
为奇函数;(3)参数方程
所表示的曲线是圆;(4)函数
,当
时,
恒成立.其中真命题的个数为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e60a44154f75c823ce1ecc9bc18928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be2585d719d74ef09632086010d6e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a050a32bde87e6e760bcc1a9b498b2c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2498db154c52793d86de198f26af0de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc67c118eb59c6b5dc1f714579ff597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d710fccfef7b297602331d89489408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9518d59e737e3ac698165c5ec17ba636.png)
A.4个 | B.3个 | C.2个 | D.1个 |
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6 . 对于定义域为R的函数
,若函数
是奇函数,则称
为正弦奇函数.已知
是单调递增的正弦奇函数,其值域为R,
.
(1)已知
是正弦奇函数,证明:“
为方程
的解”的充要条件是“
为方程
的解”;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278220a216c6b4b0656acc01484a5a97.png)
,求
的值;
(3)证明:
是奇函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181def204e869738a2f39f87a5818be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104375baf5cef5eb92cfc7cf13b80193.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dde0f01007fc21d40fab9b8c8d2521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dbaaee3ba57fa0892b185b243b5c39c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991c3d6d8843ad321f31655c63d42d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7649ab6e2530a885646af610f54ad694.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278220a216c6b4b0656acc01484a5a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe4b2c42caef444867e0dadd10bccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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7 . 设集合
、
均为实数集
的子集,记:
;
(1)已知
,
,试用列举法表示
;
(2)设
,当
,且
时,曲线
的焦距为
,如果
,
,设
中的所有元素之和为
,对于满足
,且
的任意正整数
、
、
,不等式
恒成立,求实数
的最大值;
(3)若整数集合
,则称
为“自生集”,若任意一个正整数均为整数集合
的某个非空有限子集中所有元素的和,则称
为“
的基底集”,问:是否存在一个整数集合既是自生集又是
的基底集?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eecb2784e8889eb4b245a31f1f5fa5d.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f92003c437fb47e29838ed60e3653e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce69cd33d105ce280170f0cd0513026.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352d9b76dcf639368fa68cae70149802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ba400854be8c167d7c20f11f2186a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a3f24673b6e954db3a8b229d8c4564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eded177e1ed7b4d3b9d011033d79aa1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce69cd33d105ce280170f0cd0513026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e3cdc4da74a1d01103655fa8311540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5779e9f5131f17cd24176bb6f26795db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若整数集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b282608bf96abda302bc3ff5dd10953.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52866a74e4af867ceea0efb1ad06602c.png)
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名校
8 . 设函数
;
(1)当
时,解不等式
;
(2)若
,且
在闭区间
上有实数解,求实数
的范围;
(3)如果函数
的图象过点
,且不等式
对任意
均成立,求实数
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e5128871e294842277b0df6870ff76.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2b77a47cd3c8fd4aeaafc76df266f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f2700954448bbf39e3dc5113c33f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44284ff1ea50429a0610e13363be6080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e93c03e8cf602736e073c6f0858521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d53d13da463ab77aad0337177f8d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2020-01-29更新
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3卷引用:2017届上海市宝山区高考一模数学试题
9 . 若使集合
中的元素个数最少,则实数
的取值范围是_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4908bdb7bc19131cfe6b945d3fe0f3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
10 . 对于函数
,若存在正常数
,使得对任意的
,都有
成立,我们称函数
为“
同比不减函数”.
(1)求证:对任意正常数
,
都不是“
同比不减函数”;
(2)若函数
是“
同比不减函数”,求
的取值范围;
(3)是否存在正常数
,使得函数
为“
同比不减函数”,若存在,求
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9298ea50c497b0ad0905c08d72565892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c64c9f7e6d921f2f134b832dc87e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)求证:对任意正常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75002197969b3f83acd8a964c08c1e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)是否存在正常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d6ad71a9ff62fe6cdcb3393011b64a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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2020-01-29更新
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9卷引用:上海市复旦大学附中2018届高三上学期10月月考数学试题
上海市复旦大学附中2018届高三上学期10月月考数学试题上海市复旦大学附属中学2018届高三上学期第一次综合测试数学试题上海市杨浦区2017届高三上学期期末质量调研数学试题上海市复旦大学附属中学2018 届高三上学期第一次月考数学试题上海市南洋模范中学2021届高三上学期9月月考数学试题(已下线)重难点12 选考系列(参数方程与不等式)-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)课时07 不等式的基本性质-2022年高考数学一轮复习小题多维练(上海专用)(已下线)专题02 函数的综合应用-1上海市七宝中学2023-2024学年高一下学期开学考试数学试题