1 . 已知函数
具有以下的性质:对于任意实数
和
,都有
,则以下选项中,不可能是
值的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.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/9e2469a3ff9552ad17fa8cf8b54b6d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
A.![]() | B.![]() | C.0 | D.1 |
您最近一年使用:0次
名校
解题方法
2 . 在数学中,双曲函数是与三角函数类似的函数,最基本的双曲函数是双曲正弦函数与双曲余弦函数,其中双曲正弦函数:
,双曲余弦函数:
.(e是自然对数的底数,
).
(1)计算
的值;
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
______,并加以证明;
(3)若对任意
,关于
的方程
有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3321510a9eb73909a36c084a8630e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099b9b80ed478824fa95677ebe9d5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e694af0c9f990ecb8b54b1c08bcc578e.png)
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92c32edc0e000405b7a6b9c48549959.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f78f05631a2ecb8bc3d379ca6c81f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed807cc52eca7b462a3850b5e5e02b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-06-21更新
|
1020次组卷
|
8卷引用:上海市宝山区2022-2023学年高一下学期期末数学试题
上海市宝山区2022-2023学年高一下学期期末数学试题上海市闵行(文琦)中学2023-2024学年高一下学期3月月考数学试卷(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)上海市市西中学2023-2024学年高一下学期期末复习数学试卷(已下线)模块六 专题5 全真拔高模拟1(已下线)专题14 三角函数的图象与性质压轴题-【常考压轴题】山东省济南市山东师大附中2022-2023学年高一下学期数学竞赛选拔(初赛)试题(已下线)第10章 三角恒等变换单元综合能力测试卷-【帮课堂】(苏教版2019必修第二册)
名校
3 . 设函数
的定义域为
,满足
,且当
时,
.则下列结论正确的个数是( )
①
;
②若对任意
,都有
,则
的取值范围是
;
③若方程
恰有3个实数根,则
的取值范围是
;
④函数
在区间
上的最大值为
,若
,使得
成立,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322eb46d949b9580bcc057d146b7fc58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bb7883ea87e6275472dbe14ee62357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fae0961f73fe66ddbb6a2d4c84fd5d9.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb044d6b7e232c5c39384990a1a285a.png)
②若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58640a13608e28bdba923ce9b0fc2f83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fbc901cbdb68130ddac3174583dd93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3051efcfbef4a24a467c9c87ce539399.png)
③若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a00c8bc9320947e4aba7bde335f94fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35a0af3905dfbe0020c9dd754be18dc.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88aa362994a95687a4b0702b4179e1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65db7004a3fe2d303967177f74996b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87c29eba4d978481f0a44764abb5c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c34df9793b10c5125ac05fb3f120c58.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2023-02-20更新
|
867次组卷
|
3卷引用:上海市杨浦高级中学2024届高三上学期开学考试数学试题
名校
解题方法
4 . 已知定义域为
的函数
满足:①对任意
,
恒成立;②若
则
.以下选项表述不正确 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b8e9b3f07d91da4d256d18df240fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f23544b67f1141b504123f94c1dedb.png)
A.![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.函数![]() |
您最近一年使用:0次
2023-01-12更新
|
723次组卷
|
5卷引用:上海市浦东新区2022-2023学年高一上学期期末数学试题
上海市浦东新区2022-2023学年高一上学期期末数学试题上海市吴淞中学2022-2023学年高一上学期期末数学试题上海市罗店中学2022-2023学年高一下学期3月月考数学试题(已下线)模块四 专题2 题型突破篇 小题进阶提升练(1)(已下线)期末真题必刷易错60题(28个考点专练)-【满分全攻略】(人教A版2019必修第一册)
名校
5 . 已知定义域为
的函数
满足:①对
,恒有
;②当
时,
.
(1)求
的值;
(2)求出当
,
时的函数解析式;
(3)求出方程
在
中所有解的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffe896777dc4f9aebb0e6b11ed3ed37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b8e9bb1e11d02cc2190a6e5ede4293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96c2c79f7d0a248ed590a0bce7eb8bd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166a53e132781c63d215c6c2cee3d306.png)
(2)求出当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538190cf2a2e6f248188ae111a162ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf910f82c3094b267a3d481d23d829f.png)
(3)求出方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf81798e77ead893922361d5e1d4548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5cf57d2484a1293cfd296a5ae2da1e.png)
您最近一年使用:0次
名校
6 . 已知
为定义在
上的增函数,且任意
,均有
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4138e3a956d50c217cdd4799ff1edd.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d247e7cf1e39ccef7c98fcf4442dc8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4138e3a956d50c217cdd4799ff1edd.png)
您最近一年使用:0次
名校
7 . 定义域为集合{1,2,3,…,12}上的函数
满足:
(1)
;(2)
(
);(3)
、
、
成等比数列;
这样的不同函数
的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/737818f97b6740bb592d0231b89a1810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70806d49bcdfe5f8d634e58f05b9d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df9a2654432d4e8b9e04b021361e51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cf32a49e3b54be4f9ea5baba97efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3859bc49d58f9dbf86ac4ec1af794ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080fe7b0eaf5f60d9d3bd41cf0d3071e.png)
这样的不同函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
A.155 | B.156 | C.157 | D.158 |
您最近一年使用:0次
名校
8 . 设函数
的定义域为
.若存在实数
使得
,
均对任意
成立,则称
为“
型—
函数”.
(1)若
是“
型—
函数”,求
的值;
(2)若
是“
型—
函数”,求证:函数
是周期函数;
(3)若
是“
型—
函数”,且
在
上单调递增,求证:存在正实数
、
,使得
对任意
成立.
![](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/c85f7b5cd105cfbfe19d3975fe0573a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c84c775c72661ae8ccec0a2feea257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934a66a6224413babe47db764affbffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72277254a7d7f03768d2504c9a10e02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7394c6c1b35612c4870e53ead1064aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7450ecbbe9630e42533112af3fc9de67.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23a7d274114678c90f98079a5b38df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac5b738cd5ea12f6d93e9c5fc6bcd5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72277254a7d7f03768d2504c9a10e02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2de7963cbc4da81f86019ebd64d190c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
您最近一年使用:0次
2020-09-13更新
|
621次组卷
|
4卷引用:2020届上海市高三下学期高考预测数学试题
2020届上海市高三下学期高考预测数学试题(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)上海市向明中学2022届高三上学期9月月考数学试题上海市交通大学附属中学2022-2023学年高二下学期开学考试数学试题
名校
解题方法
9 . 若
是定义在
上的函数,且对任意
都有
,
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0455ee2dc1295a05157be422968bf.png)
____
![](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/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859e341e3ee37b3028f7951ebea3ffd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/317dfdd985e880ea154da504cec0d691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a5c5e106845cc7549bc3473818d31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0455ee2dc1295a05157be422968bf.png)
您最近一年使用:0次
2020-04-11更新
|
881次组卷
|
3卷引用:上海市复旦中学2022届高三上学期9月月考数学试题
名校
解题方法
10 . 对于定义域为R的函数
,部分
与
的对应关系如表:
![](https://img.xkw.com/dksih/QBM/2020/5/9/2459073485799424/2461415147413504/STEM/1c00d3f730464fc383df57208b11693b.png?resizew=554)
(1)求
:
(2)数列
满足
,且对任意
,点
都在函数
的图象上,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d9cec7702a95b5f3378a37d3609da02.png)
(3)若
,其中
,求此函数的解析式,并求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/2020/5/9/2459073485799424/2461415147413504/STEM/1c00d3f730464fc383df57208b11693b.png?resizew=554)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f47f38e17214e09803e8c12dac0e83.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0736457346c11dd6f458418a4f747ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302b13a66072fb0e9bc6eb06a2bef202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d9cec7702a95b5f3378a37d3609da02.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1ec6a7d80a53277f35f247ac31db65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d57e3db14035c9fce38966f61e55971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4e5c9a2fbb080717f02ce7539df2f.png)
您最近一年使用:0次
2020-05-13更新
|
1081次组卷
|
15卷引用:2017届上海市虹口区高三4月期中教学质量监控(二模)数学试卷
2017届上海市虹口区高三4月期中教学质量监控(二模)数学试卷2017届上海市虹口区高考二模数学试题(已下线)上海市华师大二附中2019-2020学年高一下学期期中数学试题(已下线)上海市华东师范大学第二附属中学2019-2020学年高一下学期4月月考数学试题(已下线)考点03 三角函数与解三角形-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)第7章 三角函数【真题训练】-2020-2021学年新教材高一数学下册单元复习一遍过(沪教版2020必修第二册)(已下线)第9讲期中复习(练习)提升卷-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)(已下线)第7讲 函数y=Asin+(wx+φ)的函数的图像(练习)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)(已下线)上海期末真题精选50题(大题压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)上海市实验学校2022届高三冲刺模拟卷5数学试题江西省宜春市高安中学2019-2020学年高一上学期期中数学(A)试题山西省怀仁市2021届高三上学期期中数学(理)试题(已下线)第19讲压轴综合题(讲义)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)(已下线)期中重难点突破专题01-【尖子生专用】2021-2022学年高一数学考点培优训练(人教A版2019必修第一册)(已下线)专题06 三角函数(模拟练)-2