名校
解题方法
1 . 已知函数
,满足:①对任意
,都有
;
②对任意
都有
.
(1)试证明:
为
上的单调增函数;
(2)求
;
(3)令
,试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604c3ed013411e9434f9b09044231465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2c2b34f9a5a85e9e2d4057b3c10130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf6a72e9fa5c736a96163d1628cebb6.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407169706c508bfae5d039639b49477d.png)
(1)试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd62e0e1189886f90e0c5bc126f64a4.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cf16d7b4f5f2f8d6a1fe2d8a59538b.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2f851b643e3a77682f0196dcf3e797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18fe881244327001ef94b611e6b159db.png)
您最近一年使用:0次
解题方法
2 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14e959bd1ed92315ec2cb4b02ced581.png)
(1)求函数
的定义域;
(2)证明:
在
上为增函数;
(3)当
时,求函数的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14e959bd1ed92315ec2cb4b02ced581.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b5e402f725a71c3305bf3e72f72ded.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4bce0e9f17a187f11f8ef332cb7dd0.png)
您最近一年使用:0次
3 . 已知函数
与
有相同的定义域.
(1)解关于x的不等式
;
(2)若方程
有两个相异实数根
,且
在区间
上单调递减,证明:
.(参考结论:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3e9e7ece474b0874115b7a674e24f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce694fcd504edf03fda2504b9fc5dfd.png)
(1)解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2aabc96b7433bba077ceac76d8f0d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351629c193354cdcf202133052e45028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69dcbe710ce138ae9b04ee2969c2c28d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cafc61273b7ecebc21d0d0228168a6.png)
您最近一年使用:0次
2021-01-29更新
|
676次组卷
|
6卷引用:广东省广州市白云区(珠海区)2020-2021学年高一上学期期末数学试题
广东省广州市白云区(珠海区)2020-2021学年高一上学期期末数学试题广东省广州市第九十七中学2022-2023学年高一上学期12月阶段训练数学试题福建省莆田市第八中学2023-2024学年高一上学期第二次月考数学试题广东省东莞市东华高级中学、东华松山湖高级中学2023-2024学年高一上学期12月月考数学试题(已下线)大题专练训练39:导数(双变量与极值点偏移问题2)-2021届高三数学二轮复习(已下线)专题7.2 函数综合 B卷(常考题型精选)-2021-2022学年高一数学单元卷模拟(易中难)(2019人教A版必修第一册)
4 . 已知数集
,其中
,且
,若对
,
与
两数中至少有一个属于
,则称数集
具有性质
.
(1)分别判断数集
与数集
是否具有性质
,说明理由;
(2)已知数集
具有性质
,判断数列
,
,…,
是否为等差数列,若是等差数列,请证明;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c1d125b49fe60bc9796cf7d72e9170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550e79a4d9c549c9e28bbf30f74e24d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1906b96e054c5e74d295b61149a36b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ef5ce9b1b2850e4a95e7c0ce44bac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7152dfaf58cc9ff3df8c3d1ac7c435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
您最近一年使用:0次
名校
5 . 已知定义域为
的函数
.
(1)判断并证明该函数在区间
上的单调性;
(2)若对任意的
,不等式
恒成立,求实数
的取值范围;
(3)若关于
的方程
有且仅有一个实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7915b6900ac6c66add5e839a44fe0403.png)
(1)判断并证明该函数在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b029e85e686623cdef977b2cb1f207a.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7179b23c62085ddec400418edcde30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d7b402546bce342251322cc0655834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6868fab6404f9fd582f668343e1309a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2020-11-24更新
|
642次组卷
|
3卷引用:江苏省无锡市江阴高级中学2020-2021学年高一上学期12月学情检测数学试题
名校
解题方法
6 . 定义在R上的函数f(x)满足:
x,y∈R,f(x-y)=f(x)+f(-y),且当x<0时f(x)>0,f(-2)=4.
(1)判断函数f(x)的奇偶性并证明;
(2)若
x∈[-2,2],a∈[-3,4],f(x)≤-3at+5恒成立,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dac463bbb7375dbf8e2246f9a6f0d9.png)
(1)判断函数f(x)的奇偶性并证明;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dac463bbb7375dbf8e2246f9a6f0d9.png)
您最近一年使用:0次
2020-11-18更新
|
805次组卷
|
5卷引用:湖北省黄冈市麻城市第二中学2020-2021学年高一上学期12月月考数学试题
名校
解题方法
7 . 设函数
的定义域为
,若
满足条件:存在区间
,使
在
上的值域为
,则称
为“不动函数”.
(1)求证:函数
是“不动函数”;
(2)若函数
是“不动函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0195f699765021e2c6ea985e487971.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/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37a2adb69dc49bb586de6477a1e36aa.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da0897834a1273804c2fbdce72d662e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2020-05-01更新
|
247次组卷
|
2卷引用:湖南省株洲市第二中学2019-2020学年高一上学期阶段性考试数学试题
名校
8 . 已知定义在R上的函数f(x)满足:对任意
都有
,且当x>0时,
.
(1)求
的值,并证明
为奇函数;
(2)判断函数
的单调性,并证明;
(3)若
对任意
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f55009062fdb3873a3ba4334ebd240a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a414b95cb362b1e9a251977c36b452b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb33bd0de6bd59f35f3098b28e1714a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2020-04-25更新
|
1285次组卷
|
4卷引用:江西省宜春市宜丰县宜丰中学2019-2020学年高二下学期第一次月考数学(文)试题
江西省宜春市宜丰县宜丰中学2019-2020学年高二下学期第一次月考数学(文)试题湖北省黄冈市麻城市2019-2020学年高一上学期期中数学试题江苏省苏州市高新区第一中学2021-2022学年高三上学期10月月考数学试题(已下线)专题4.1 指数与指数函数(B卷提升篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教B版)
名校
9 . 设函数
的定义域为
.若存在实数
使得
,
均对任意
成立,则称
为“
型—
函数”.
(1)若
是“
型—
函数”,求
的值;
(2)若
是“
型—
函数”,求证:函数
是周期函数;
(3)若
是“
型—
函数”,且
在
上单调递增,求证:存在正实数
、
,使得
对任意
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85f7b5cd105cfbfe19d3975fe0573a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c84c775c72661ae8ccec0a2feea257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934a66a6224413babe47db764affbffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72277254a7d7f03768d2504c9a10e02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7394c6c1b35612c4870e53ead1064aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7450ecbbe9630e42533112af3fc9de67.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23a7d274114678c90f98079a5b38df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac5b738cd5ea12f6d93e9c5fc6bcd5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72277254a7d7f03768d2504c9a10e02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2de7963cbc4da81f86019ebd64d190c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
您最近一年使用:0次
2020-09-13更新
|
618次组卷
|
4卷引用:2020届上海市高三下学期高考预测数学试题
2020届上海市高三下学期高考预测数学试题(已下线)热点02 函数及其性质-2021年高考数学【热点·重点·难点】专练(上海专用)上海市向明中学2022届高三上学期9月月考数学试题上海市交通大学附属中学2022-2023学年高二下学期开学考试数学试题
名校
解题方法
10 . 已知
是定义在
上的函数,满足
.
(1)证明:2是函数
的周期;
(2)当
,
时,
,求
在
,
时的解析式,并写出
在
,
时的解析式;
(3)对于(2)中的函数
,若关于
的方程
恰好有20个解,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/c7b94f154fad04efe8c4af84831ee43b.png)
(1)证明:2是函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3038d4728f959a8efedc2592e4a4b5fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17bd7834d6f17e5f30f10ca4b562552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fb378d6bf91902efa15881985c5e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63fda4ef593f6f4bc7cf7c5ecabd584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2db1cf3233339a322fbe52ada4ddd7.png)
(3)对于(2)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e9ecfdf2ec90ea96e104158aec81c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-08-13更新
|
1394次组卷
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6卷引用:上海市实验学校2018届高三上学期第二次月考数学试题
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