解题方法
1 . 已知函数
是定义在区间
上的奇函数,且
,若对于任意的m,
,
,有
.
(1)判断函数的单调性(不要求证明);
(2)解不等式
;
(3)若
,存在
,对于任意的
恒成立,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c9462c98381290a22e97c993ad7108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ceab25570ede0db9cfce6020fc40ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4440dae5b564c68d767e66a7481d943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef7f1625721af5314e8518f26c080e1.png)
(1)判断函数的单调性(不要求证明);
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d15d1aadb3d6cfbda8dba46bcce3d1a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982a6ec26dedf89e72ddaabfa6670183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10dd628a48cf11a09a49d38b40d1ce26.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
.
(1)用定义证明函数
在R上是减函数;
(2)探究是否存在实数a,使得函数
为奇函数?若存在,求出a的值;若不存在,请说明理由;
(3)若
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe01922147e7a0b3948344bcb2828f0.png)
(1)用定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)探究是否存在实数a,使得函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a38f9436fa939f0c482a2aa67cfdde.png)
您最近一年使用:0次
2020-02-13更新
|
377次组卷
|
2卷引用:河北省石家庄市第一中学2019-2020学年高一上学期期末数学试题
名校
3 . 已知函数
是定义在
上的函数.
(1)用定义法证明函数
的单调性;
(2)若关于x的不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112675a07ab5e2227c2f872b313a2b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
(1)用定义法证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ea2aec5fcb690f58dc7f33d5b7d140.png)
您最近一年使用:0次
2020-02-03更新
|
342次组卷
|
5卷引用:【市级联考】四川省攀枝花市2018-2019学年高一上学期期末教学质量监测数学试题
19-20高一上·江苏·阶段练习
4 . 已知函数
是定义在
上的奇函数,且
.
(1)求
的值;
(2)判断函数
在区间
上的单调性,并用定义证明;
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5bec6e5f8997197659647dda1c6fe9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc47f2786ed178c1bcf8ff13bfc4739.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a8c0e96d50acaecca352e93709f78f.png)
您最近一年使用:0次
11-12高一上·河南许昌·期末
名校
5 . 若非零函数
对任意实数
均有
,且当
时,
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)求证:
为减函数;
(3)当
时,解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db7387dec34f24cacb1cd95c433e8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e37c94f22f621f6952e100cd6c2d3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4422ee238e091b2f58a9aa4ca0c7a11.png)
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解题方法
6 . 已知函数
.
(1)判断函数
在区间
和
上的单调性(不必证明);
(2)当
,且
时,求
的值;
(3)若存在实数
,使得
时,
的取值范围是
,
求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa227c11b63f18792c94265c8cf2452.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f26f6cc6cf7d49eeffa37036436bc54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f0a7f52eb82472cce50381cbed1c16.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94345694d4215284c41f87146795ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7266b2ef457b8ddeee3fa2cc24022e.png)
(3)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c90ddcd8f9815d080848ab860d1225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70128385b9ab66ac44614af35a0dcdce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254cf38cf25199e307b85d19a3c456b4.png)
求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7266b2ef457b8ddeee3fa2cc24022e.png)
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7 . 已知函数
,
,且
.
(1)证明函数
在区间
上是增函数;
(2)设函数
. 若区间[2,5]是
的一个单调区间,
且在该区间上
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7590785d8ee40f3d7206d4aa819265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2817c52144d06555e98131b5e657c4.png)
(1)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad24b182074510c1952e5948a6f8230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
且在该区间上
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee31b9dffcd91ff2f5477410bc09f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
8 . 已知定义在区间
上的函数
,其中常数
.
(1)若函数
分别在区间
上单调,试求
的取值范围;
(2)当
时,方程
有四个不相等的实根
.
①证明:
;
②是否存在实数
,使得函数
在区间
单调,且
的取值范围为
,若存在,求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c9eca1510647f9b40cf7ce69c3757f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26337502f8a07b4655416be99c2c09b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
(1)若函数
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792483540934656/1793041726971904/STEM/6318e0e1e1f84a3da44c6ac2c1beaef2.png?resizew=36)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e670e88873b35b46ad6d193d8a55e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16df3112ff53691d26bca57f85cdc3b.png)
②是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792483540934656/1793041726971904/STEM/6318e0e1e1f84a3da44c6ac2c1beaef2.png?resizew=36)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792483540934656/1793041726971904/STEM/6318e0e1e1f84a3da44c6ac2c1beaef2.png?resizew=36)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8af7bed124f00c8e19b52d028b4d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-03更新
|
1136次组卷
|
4卷引用:2015-2016学年湖北宜昌市一中高一上期中考试数学试卷
14-15高一上·广东惠州·期末
9 . 已知函数
满足:对任意
,都有
成立,且
时,
.
(1)求
的值,并证明:当
时,
;
(2)判断
的单调性并加以证明;
(3)若
在
上单调递减,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922c4a02ab7b24cb1c6ccdccb6d08353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb1dc30d4b297c6d5d0d6d91eab1e3b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6a2389254f9c43bbb0bf8f4abcc90a.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27539a750d94c03c9832b13dc2d6674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6ffa6fe2387ee19234c2ad0fcb92ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2016-12-02更新
|
1475次组卷
|
6卷引用:2013-2014学年广东惠州市高一第一学期期末考试数学试卷
(已下线)2013-2014学年广东惠州市高一第一学期期末考试数学试卷2015-2016学年黑龙江省海林林业局一中高一上学期期末考试数学试卷2017届福建连城县朋口中学高三上期中数学(理)试卷2016-2017学年辽宁省六校协作体高二下学期期初数学(理)试卷(已下线)2019年7月16日 《每日一题》2020届高考一轮复习(理科)—— 函数的单调性与最值(已下线)2019年7月16日 《每日一题》2020届高考一轮复习(文科)—— 函数的单调性与最值(1)
11-12高一·辽宁大连·期末
解题方法
10 . 已知函数
满足对一切
都有
且
,当
时有
.
(1)求
的值;
(2)判断并证明函数
在
上的单调性;
(3)解不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b161d1fa052b4b7b1d991da282b6bf84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a1ec7bcc711bfc514425c7a976fe8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196be101149acfb6a6c4ceca7fc96828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b530377e3fe56b7988935dd73d9dccd.png)
(2)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
(3)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb33ccd9040a106849d16dd178d98b29.png)
您最近一年使用:0次