名校
解题方法
1 . 已知函数
=![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8679efcfb7e951bc73368ca1b49a77.png)
(1)若a=4,判断函数f(x)在定义域上的单调性,并利用单调性定义证明你的结论.
(2)若函数
在区间
上单调递减,写出a的取值范围(无需证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8679efcfb7e951bc73368ca1b49a77.png)
(1)若a=4,判断函数f(x)在定义域上的单调性,并利用单调性定义证明你的结论.
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b5e402f725a71c3305bf3e72f72ded.png)
您最近一年使用:0次
2020-10-23更新
|
129次组卷
|
2卷引用:浙江省金华市东阳中学2020-2021学年高一上学期10月阶段考试数学试题
名校
解题方法
2 . 已知函数
(
).
(1)若
是奇函数,求实数a的值;
(2)判断
的单调性,并用单调性的定义证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd492d001a460384ca5c5ad7211561f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
3 . 若函数
在定义域内的某个区间
上是增函数,而
在区间
上是减函数,则称函数
在区间
上是“弱增函数”.
(1)分别判断
,
在区间
上是否是“弱增函数”(不必证明);
(2)若函数
(
、
是常数)在区间
上是“弱增函数”,求
、
应满足的条件;
(3)已知
(
是常数且
),若存在区间
使得
在区间
上是“弱增函数”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e82cc461b9607e08a8b31597f6d26df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09723a50d2bce12318e1b9b2c5c02621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dccd78102e7372f800abeb4eb0e2f99a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154186900500104502219afe07839158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445417d66161e8f8cbe9fb2166de74fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659340c5560a41e799f1ee06aa58a01c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
4 . 已知定义在区间
上的函数
.
(1)判断函数
在
的单调性,并用定义证明;
(2)设方程
有四个不相等的实根
,
,
,
.
①证明:
;
②在
是否存在实数a,b,使得函数
在区间
单调,且
的取值范围为
,若存在,求出m的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3b7dad914220ef1fce0949762424f31.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47265a7db6d8578072058da7952589b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b5e402f725a71c3305bf3e72f72ded.png)
(2)设方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb2e46f49adba6036e2624639a1b966.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16df3112ff53691d26bca57f85cdc3b.png)
②在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dccf1f9faac56117d6d3dd1dddd286d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ac459b9a998401442d80e2970c6f5e.png)
您最近一年使用:0次
2020-10-12更新
|
938次组卷
|
5卷引用:江西省南昌市江西师大附中2019-2020学年高一上学期10月月考数学试题
解题方法
5 . 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
解题方法
6 . 已知奇函数
.
(1)求实数
的值;
(2)判断函数
在其定义域上的单调性,并用定义证明;
(3)若
对所有的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ee519de937792a2b0b21d52b9a2e86.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc39dad5c7d43f084dcfc261089c37c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36c9c91220b0f2cbd4a48e8fa90e3d.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
7 . 已知函数
是定义域为
的奇函数,且在
上单调递增.
(1)求证:
在
上单调递增;
(2)若不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1c92c42188e3b2cb800d1186eab12.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8a10b19bd40d8a81d88a6013f4d476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-02-28更新
|
231次组卷
|
2卷引用:甘肃省兰州市第五十一中学2019-2020学年高一上学期期中数学试题
名校
解题方法
8 . 已知函数
.
(1)用定义证明
在区间
上是减函数;
(2)若不等式
对任意的
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5effb3053cf609f59178641cd48167.png)
(1)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55762dbc5015e3c5f7cfd894c6dea023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c22892cd526d878e3a022e4451f948c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-04-30更新
|
260次组卷
|
2卷引用:安徽省六安市第一中学2019-2020学年高一上学期第一次段考数学试题
名校
9 . 设
是定义在
上的函数,且对任意
,恒有
.
(1)求
的值;
(2)求证:
为奇函数;
(3)若函数
是
上的增函数,已知
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd384d86840b7b158af41f56fe29c7d1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d359b23b6fe29a0f10758c6130315b4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-12-14更新
|
3188次组卷
|
4卷引用:四川省宜宾市第三中学2019-2020学年高一上学期10月月考数学试题
四川省宜宾市第三中学2019-2020学年高一上学期10月月考数学试题黑龙江省伊春市伊美区第二中学2019-2020学年高一上学期第一次月考数学试题(已下线)专题04函数的奇偶性解题模板(已下线)突破3.2 函数的基本性质(重难点突破)
名校
解题方法
10 . 已知函数
的定义域是R,对任意的实数m,n,都有
,且
,当
时,
.
(1)求
,
,
;
(2)判断函数
的单调性,并证明;
(3)若
对任意的
恒成立,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60bc03c54f5fe0cbea41e3f1e1b917f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8dfda35f1dc37e92b20d67219aa91e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a039b83b7784132b820a32c9894a2b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e1a1611f320c0f358df77aaae3f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf59c5075f9e6fdf3782b6c0e528237.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c50e1c5263ee5567069d003d970535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36c9c91220b0f2cbd4a48e8fa90e3d.png)
您最近一年使用:0次