1 . 已知函数
.
(1)判断并证明函数
的奇偶性;
(2)判断函数
在定义域上的单调性,并用单调性的定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66762b46532b9c7224ce11eb3265f60.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
解题方法
2 . 设
,
.
(1)判断
的奇偶性,并证明;
(2)写出
的单调区间(直接写出结果);
(3)若当
时,函数
的图象恒在函数
的上方,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f70345d77b92867c548f44deae4891e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3f0e295cc6fa40b8aaad1049e1f01f.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c735550bf19096ef02e7cc05b40a0879.png)
(3)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8408a1b2a46ac429c5398500b6223f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f466a93c9e7acd29a0b5790668124f4a.png)
您最近一年使用:0次
2024-01-06更新
|
424次组卷
|
3卷引用:江西省上饶市广丰区私立康桥中学2023-2024学年高一上学期期末模拟数学试题
江西省上饶市广丰区私立康桥中学2023-2024学年高一上学期期末模拟数学试题(已下线)高一数学开学摸底考 01-人教B版2019必修第一册+第二册摸底考试卷吉林省白山市2023-2024学年高一上学期期末教学质量监测数学试卷
名校
3 . 已知函数
.
(1)求函数
的定义域,
(2)判断并证明函数
的奇偶性,
(3)判断函数
的单调牲(只写出结论即可),并求当
时,函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bdae0a49cb70f74c5cd89defaacdfdc.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7153aeeff11bfa0bb5f064d4edb66ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
解题方法
4 . 已知函数
.
(1)求
的定义域;
(2)判断
的奇偶性,并证明;
(3)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2d1867282f5cd284216f46bc23b2e3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
您最近一年使用:0次
名校
解题方法
5 . 设函数
.
(1)当
时,求
的值;
(2)判断
在区间
上的单调性,并用函数单调性的定义证明你的结论;
(3)当
时,
的最小值为3,求m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9088a940f6c06449d4fed2d29d3b56dd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48350c9f896c18a64f27867ca81c9be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2024-01-20更新
|
219次组卷
|
2卷引用:北京市朝阳区2023-2024学年高一上学期期末质量检测数学试题
名校
解题方法
6 . 设集合
存在正实数
,使得定义域内任意x都有
.
(1)若
,证明:
;
(2)若
,且
,求实数a的取值范围;
(3)若
,且
,求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a293f8a5cb9cb0d905ca25a01faefc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b452eaa74ef4e90a6661350333df7e49.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb1ba12c3538ad16ac98407658246f0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021f43d4d536af9301adad72758d3355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764df344e05f8ef1a97b346ddf44a5a0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7974d7d586f9697ad00b34ce5ada820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9511a2031188decf655cdfc0302b4740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
您最近一年使用:0次
7 . 设函数
,
.
(1)判断函数
的奇偶性,并证明;
(2)写出函数
的单调区间(直接写出结果);
(3)若
,使
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5649d1b1f611385016e25b6409bdea5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac0eb0ec6bd320f34e03008444d924f.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae69f34beea60ab5919034a7b44934e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85544d5708b61d729152499860334fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd70f369f90b1770cd4b290c5ad78b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
8 . 已知数列
,满足
且点
在函数
的图像上,且
.
(1)证明:
是等比数列.并求
.
(2)令
,设
的前
项和
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a189f5f230b75af75eed2a5ff0f24b1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69b76612264b62b3e66947e71707ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88aef647186022d30b0e719126d6465.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d8f2f15adae9848373de1ab8c7bc7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e9c7610cbf2bda17bd7206969fb599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105de1b20942840a12712c6795a05e1b.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
的单调递减区间为
,函数
.
(1)求实数
的值,并写出函数
的单调递增区间(不用写出求解过程);
(2)证明:方程
在
内有且仅有一个根
;
(3)在条件(2)下,证明:
.
(参考数据:
,
,
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387a35447fe9069587d70c9bf9aca4da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e10140ab3cdc13d710a65b2287c892b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87296504fd8313d1c10842e4db22ea1a.png)
(2)证明:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a3e2f00d1df62b3114f03f20877c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d655ee6d4c2285b6f59652360862d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)在条件(2)下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4287d11737a987758112fb7494cc12fd.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594663e98b797cdc4efbd098cc15854f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb92b2f1b067084b3eb3103bb1353520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b7cfcc147916ae7eeb5d557fea945e.png)
您最近一年使用:0次
2023-11-30更新
|
623次组卷
|
3卷引用:江西省赣州市龙南市阳明中学2023-2024学年高一上学期期末模拟训练数学试题(二)
2023高一上·全国·专题练习
名校
解题方法
10 . 已知函数
且
.
(1)求
的定义域,判断
的奇偶性并给出证明;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82da026cf6076d8009620698b0f1cb31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fbf4529d247ae8d2e82db507833931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-11-26更新
|
1203次组卷
|
5卷引用:广东省高州市某校2023-2024学年高一上学期期末学情数学练习卷
广东省高州市某校2023-2024学年高一上学期期末学情数学练习卷云南省曲靖市民族中学2023-2024学年高一上学期期末考试数学试卷(已下线)模块一 专题1 对数与对数函数(人教A)2(已下线)3.2~3.3对数函数的图象和性质-同步精品课堂(北师大版2019必修第一册)辽宁省朝阳市建平县实验中学2023-2024学年高一上学期12月月考数学试题