1 . 已知函数
.
(1)判断
的奇偶性并证明;
(2)用函数单调性的定义证明
在区间
上单调递增;
(3)若对
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fbfe19b6da085fc850cf18c3ff365c.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用函数单调性的定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f851f7b4f5386142f46c899bbb58b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc01a41151030e7e596bc9bdfd65812b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
21-22高一下·江苏南通·开学考试
名校
解题方法
2 . 已知函数
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b3507f33c70ab49d30df52c8b82b60.png)
(1)若
的最小值为
,求
的值;
(2)若存在
,使
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63669c403ba7972d296968395ef293de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b3507f33c70ab49d30df52c8b82b60.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97ab84192e12bb292bc9fbd0b29fbee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac32bfa7f2ef6610bd22bfda1294f5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-02-28更新
|
927次组卷
|
6卷引用:江苏省南通市如皋市2021-2022学年高一下学期期初调研测试数学试题
名校
3 . 已知函数
.
(1)求
的值;
(2)求函数
的值域;
(3)若
,且对任意的
、
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b897d42526be27494db78f685d09ca88.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7644c1e19089a00e3f630f82dcb7244.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1029cd644917b65c419fe372cd5db2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33890c6b0bf167514d44139d9dca0154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcef2da543513a6176d17d271f7ebf43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-02-10更新
|
511次组卷
|
4卷引用:广东省深圳市光明区2021-2022学年高一上学期期末数学试题
名校
解题方法
4 . 在数学中,双曲函数是一类与常见的三角函数类似的函数,最基本的双曲函数是双曲正弦函数和双曲余弦函数(历史上著名的“悬链线问题”与之相关).记双曲正弦函数为f(x),双曲余弦函数为g(x),已知这两个最基本的双曲函数具有如下性质:
①定义域均为R,且f(x)在R上是增函数;
②f(x)为奇函数,g(x)为偶函数;
③
(常数e是自然对数的底数,
…).
利用上述性质,解决以下问题:
(1)求双曲正弦函数和双曲余弦函数的解析式;
(2)求函数
,
的值域;
(3)设
,若对任意的正数
,
,都有
,
,且
,求实数m的取值范围.
①定义域均为R,且f(x)在R上是增函数;
②f(x)为奇函数,g(x)为偶函数;
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87dd0c1b905f89e034682e5c2efa16fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
利用上述性质,解决以下问题:
(1)求双曲正弦函数和双曲余弦函数的解析式;
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754a37d25ca48536e2fd0a04ef35bf3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12228ea33b087a9b07d2c0db8822ed5f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08e2e4251169d65c400d0e420454508.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/6f5e09bc267abd01932badf72856344b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfdc108ed26f6740e2caf5cdddcf6d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8332aabdd6f54ca7333e41798f3b54.png)
您最近一年使用:0次
2022-02-06更新
|
665次组卷
|
2卷引用:江苏省常州市溧阳市2021-2022学年高一上学期期末数学试题
名校
解题方法
5 . 已知函数
,且
的解集为
.
(1)求函数
的解析式;
(2)设
,若对于任意的
、
都有
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5109b591b55b04ab757a7abb47bb8cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beea86c109b4e61a3530daba65c9e40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403e268aa7ae4cbaa883020acca4f7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a5bab6f0927d17d318b07c9e2bfffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2022-01-30更新
|
792次组卷
|
2卷引用:广东省广州市华南师范大学附属中学2021-2022学年高一上学期期末数学试题
解题方法
6 . 已知函数
(其中
,
为常数)的图像经过点
,
.
(1)试比较
与
的大小;
(2)若对于
,不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2acba9c2c7ca34589d1de4d044b46d2.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/f0002593d184f52babed474e8111902d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bdd2e972e124522d85bec5ee22bad8e.png)
(1)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cf911c6d30473af731beb1b716a0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbaf830241defed27d5ad149fb368370.png)
(2)若对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3add1679c27392a1a7f635723a4b36eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976800897a939ffb1a34518f2efe9281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
7 . 已知定义域均为
的函数
和
,
是偶函数,
是奇函数,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bb1f5200b0c319dc249305c11d9768.png)
(1)求
解析式;
(2)判断
在
的单调性,并用定义证明;
(3)若
,关于
的不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.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/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bb1f5200b0c319dc249305c11d9768.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7ed14eebfeff00a1879479c0ac0878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fede49ba75434f2795339a065c81f4bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-01-22更新
|
820次组卷
|
3卷引用:辽宁省营口市2021-2022学年高一上学期期末数学试题
名校
8 . 已知函数
,
.
(1)当
时,不等式
恒成立,求实数a的取值范围;
(2)当
时,求函数
在区间
上的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07028cbc5469ca3dc089d79b1fb0ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e9eed54554b0ecd5d2c5cdc5da6391.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43dfe6b3c337df06cfa8ffa774ed5627.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
,且
.
(1)求
及
的值;
(2)判断
的奇偶性并证明;
(3)若当
时,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa8f957203548b2f3938f90edcab966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a98186dcca4e3093a3e910b705b087.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14be574d4eaf7f7e0d2b28ade7f3ea1.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf2ed2c35711704a14db5a6c7c270f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-01-15更新
|
491次组卷
|
3卷引用:海南省2021-2022学年高一上学期学业水平诊断期末数学试题
名校
10 . 定义在
上的奇函数
,已知当
时
(
).
(1)求
在
上的解析式;
(2)若存在
时,使不等式
成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e99bebf8db0d314aacb2cb1f09bf48c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16627a6c8ecdc63f57bd822efeecb734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c1245b0dfd4fe5623a7e2dfb21e82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141f2ad9e03ece6b97f6b1d490c2e3e4.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7d2bb9fd6de312a742ef10c81b9b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea068e771b851aca8f36ea19e7e81f62.png)
您最近一年使用:0次
2022-03-30更新
|
313次组卷
|
3卷引用:河南省漯河市漯河实验高级中学2021-2022学年高一上学期第二次月考数学试题