名校
解题方法
1 . 已知函数 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89cae3b13d088c4e26a975d5ecd84166.png)
(1)求函数
的零点;
(2)证明: 函数
在区间
上单调递增;
(3)若
时,
恒成立,求正数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89cae3b13d088c4e26a975d5ecd84166.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明: 函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d90e576fd32d7cfd284d82ce54ca51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-10-10更新
|
1397次组卷
|
4卷引用:北京市陈经纶中学2023-2024学年高一上学期10月月考数学试题
2 . 下列函数中,哪些满足性质
或
?为什么?
(1)
;
(2)
;
(3)
;
(4)
;
(5)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5f197a14e1d903d4e822388798f56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdca802890b6e64cd5aaea5ef55d4d91.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec84404bbf6cf4a9d992e1760dcfdd4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3daad3a31a3597f75fa109736ed2ebf.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3cc66b811ad2395efe04d93b61c711.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c9320d009a17deba67f208c7d8be8c.png)
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解题方法
3 . 判断下列函数的奇偶性,并加以证明:
(1)
;
(2)
;
(3)
;
(4)
;
(5)
;
(6)
;
(7)
;
(8)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b6a91900d0dfa6296cdee22fdd6fe6.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6646ee1281b3b22e6a6ded9da1f9b3.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa53b1acf2f52cc408f093720b3680f.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5124e480e0bfffd64470c288ede9f51b.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629687de99fd63ec04c94ffb15b7e945.png)
(6)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68af49a6c0839e9b8a1e35b44fbc437.png)
(7)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1991c1648dec3527e23636f922d3d9.png)
(8)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3ceaea7ce559026c96525a2b4577c4.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
,且
.
(1)求
的值;
(2)证明函数
在区间
上是减函数,并指出
在
上的单调性;
(3)若对
,总有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b765990cc5e6c364362717f2ae1001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa269a448aec9dc7d6c73af33456763a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a475fec8ded321e10a6697319fb975.png)
(2)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(3)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b79d19d2037063d3b8427df8d7b6695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf7a0098d4ea8a0ad76dab74698fcb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
5 . 已知函数
,且
时,总有
成立.
(1)求
的值;
(2)判断并用定义法证明
的单调性;
(3)若关于
的不等式
在
上有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbceffd6fb3d230379384a0bb8b86acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1db6c94b94afc372212a81cc1f4dd9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)判断并用定义法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a82f9ed1fed1e3aa42434da4671b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
6 . 设函数
(
),满足
,且对任意实数x均有
.
(1)求
的解析式;
(2)当
时,若
是单调函数,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc597472ad40bcb1aecbdcc5e3f3524d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a5c5e106845cc7549bc3473818d31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679c9edadb198dae2983e88f9ee58beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234a61f2ec6806d0832e635826119ad.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
,当
时,
的图象如图.
![](https://img.xkw.com/dksih/QBM/2021/12/30/2883792866934784/2886307706036224/STEM/a60f5ae3fd8c4ed19d69766973989f34.png?resizew=374)
(1)判断并证明函数
的奇偶性;
(2)写出函数
的单调区间(直接写出结果);
(3)试讨论函数
在区间
上的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3f58722394cad3df7234b543be4587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/2021/12/30/2883792866934784/2886307706036224/STEM/a60f5ae3fd8c4ed19d69766973989f34.png?resizew=374)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)试讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da3703048188247f41c377c217c0e55.png)
您最近一年使用:0次
解题方法
8 . 已知函数
(
,
为常数),且满足
,
.
(1)求函数
的解析式;
(2)若对任意的
,关于
的不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c9f53354147c82ec29609d8ab1e04d.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/64825514b3bfdafee1c955dccfeca4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae1f4e90bf02914379c24cb8e513c75.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0097b2a40fd339906bb03607246d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1da102d7e849a7aa87b0202e5a13d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2021-11-15更新
|
1395次组卷
|
6卷引用:广东省深圳市深圳艺术学校2021-2022学年高一上学期期中数学试题
广东省深圳市深圳艺术学校2021-2022学年高一上学期期中数学试题(已下线)专题03 《函数概念与性质》中的易错题(1)-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)北师大版(2019) 必修第一册 名校名师卷 第六单元 函数的单调性和最值、函数的奇偶性与简单的幂函数A卷2023版 苏教版(2019) 必修第一册 名校名师卷 第七单元 函数的单调性、函数的奇偶性(A卷)2023版 湘教版(2019) 必修第一册 名师精选卷 第六单元 函数的基本性质A卷(已下线)第3章 函数概念与性质(基础、典型、新文化、易错、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)
解题方法
9 . 已知函数
.
(1)判断
的单调性,并用定义证明你的判断;
(2)
,若不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea366268bda7a58cace1afb754b18788.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4480b0370037df7d02a9f00a51c98505.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50a9aa56f04f429c15f66fa18f65dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
对任意的实数m,n,都有
,且当
时,有
.
(1)求证:
在R上为增函数
(2)若
,且关于x的不等式
对任意
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053e4e1dc1431145c998c014b8fc0c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e7b359eb7cd04493fc030a87eccbf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e66262160ee5ce53f9654a20682f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305dde0e78d0aa1fd43a7b09f5f46d8c.png)
您最近一年使用:0次