1 . 已知函数
.
(1)判断
的奇偶性,并说明理由;
(2)判断
在区间
上的单调性,并用定义证明;
(3)求函数
在
上的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4a76de7035cad30b98a72986bf80aac.png)
(1)判断
![](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/879234adbae93aa72b7e101b3738d4e0.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bacbd8f85c7ed750646ecf8f5b11071.png)
您最近一年使用:0次
解题方法
2 . 已知定义在
上的函数
满足
,且对任意
.
(1)证明:
在
上单调递减;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2ee8b29eae5cc48a9f7d3fd0693799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c11fa98ba9deedbdf1345f3cbec386c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37d5fed09c3fdff3d3783f8a3be2950.png)
您最近一年使用:0次
2024-01-16更新
|
372次组卷
|
2卷引用:重庆市2023-2024学年高一上学期期末数学试题
名校
解题方法
3 . 已知定义在
上的函数
满足:当
时,
,且对任意的
,
,均有
.若
,则
的取值范围是(e是自然对数的底数)( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773932788bfccf3f2a43207a159c33c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948028e81a47b4aa3fef24147259e88f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a6079c297a3db7b48fdc45a36ca4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-01-15更新
|
297次组卷
|
2卷引用:重庆市永川中学校2023-2024学年高一上学期期末复习数学试题(二)
名校
解题方法
4 . 已知
是二次函数,不等式
的解集是
,且
在区间
上的最大值是12.
(1)求
的解析式;
(2)试判断函数
在
上的单调性,并用单调性的定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c76c41773aae617db1c0cc04bcf836f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9430ded94aee51af5a5de91fef1d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef1b322a7e2dbe40f17a0f9c61ec4aa.png)
您最近一年使用:0次
2024-01-10更新
|
298次组卷
|
4卷引用:重庆市开州区临江中学2023-2024学年高一上学期第二阶段性(12月期中)考试数学试题
重庆市开州区临江中学2023-2024学年高一上学期第二阶段性(12月期中)考试数学试题江西省上饶艺术学校2023-2024学年高一上学期12月月考数学试题(已下线)专题04 函数的性质与应用2-期末复习重难培优与单元检测(人教A版2019)(已下线)3.2.1单调性与最大(小)值(第2课时)
名校
5 . 已知函数
.
(1)证明:
是奇函数.
(2)根据定义证明
在区间
上单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea40c101e6ff5f1db6cd5bdd93969b56.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)根据定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
您最近一年使用:0次
2024-01-08更新
|
372次组卷
|
3卷引用:重庆市云阳县、梁平区等地学校2023-2024学年高一上学期12月联考数学试题
名校
解题方法
6 . 定义在
上的函数
同时满足以下条件:
①
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5696ed57434e24cae4d8c521d788cfbb.png)
③
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840711b169e820b1c2a22b468711abdf.png)
则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5696ed57434e24cae4d8c521d788cfbb.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6de25fc53b7c759f260109d9dfbd8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840711b169e820b1c2a22b468711abdf.png)
则下列说法正确的有( )
A.若![]() ![]() | B.方程![]() ![]() |
C.若![]() ![]() | D.![]() |
您最近一年使用:0次
2024-01-07更新
|
230次组卷
|
2卷引用:重庆市拔尖强基联盟2024届高三上学期12月月考数学试题
名校
7 . 函数
的定义域为
,对任意的
,都有
成立,且函数
为偶函数,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/e456611ca4848715617bc9bcb215e63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657e5274d2867b47c602c36a48ec1835.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-12-28更新
|
197次组卷
|
2卷引用:重庆市三峡名校联盟2023-2024学年高一上学期数学联考试题
名校
8 . 已知函数
.
(1)证明:函数
在区间
上单调递增;
(2)判断函数
的奇偶性;(不需要证明)
(3)若
时,记函数
的最大值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98348a6484adcce636bb7220a69d8678.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66df733dcc9b6f199e6ba81ca156f075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82a1224e47f31ecdfffd328d5a3ab6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82a1224e47f31ecdfffd328d5a3ab6d.png)
您最近一年使用:0次
名校
解题方法
9 . 已知定义域为R的函数
满足
,当
时,
.若
,使
成立,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b691121b6d3bcf5c293f6aff324eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48350c9f896c18a64f27867ca81c9be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad91e04a5faf7bc002d8bd42cd4a734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3062f070934e9c23db24e9bf46e160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3460b525772deaa45309717d3ae5196c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
10 . 已知函数
的定义域为
,且满足
.对定义域内的两个任意
满足
.当
时,有
.
(1)求
,
的值.
(2)若不等式
在区间
恒成立.求
的最大值.
![](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/6b4ed4485745f1d259a3953c242b9cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938308ceead1a6a87920b457f4646f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a57d6d7b74ae630e6ce3b43afe6060.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54bd888bfb31bdd6cddc28e687304406.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08063791dbe3c3263a76c95c06d89677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次