名校
解题方法
1 . 若存在常数
、
,使得函数
对于
同时满足:
,
,则称函数
为“
”类函数.
(1)判断函数
是否为“
”类函数?如果是,写出一组
的值;如果不是,请说明理由;
(2)函数
是“
”类函数,且当
时,
.
①证明:
是周期函数,并求出
在
上的解析式;
②若
,
,求
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121706e56023722591922af58fd1dd79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5858dba99d7612311e93a49da16aaae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297c81c2628b05a8f67744ddf04e9851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e46371f310e03a153a1698aad9d4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb72ca96da578351e459f9ce3dbe44d.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1417a39c99b1e6b489c7c033a0625af.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc076c7f73dc9b6138bc40252cbbf22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2024-03-15更新
|
281次组卷
|
2卷引用:湖南省长沙市长郡中学2023-2024学年高一下学期寒假检测(开学考试)数学试题
名校
解题方法
2 . 已知函数
的定义域为
,
,
,且
在区间
上单调递减.
(1)求证:
;
(2)求
的值;
(3)当
时,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c7798e8266916b8501e3837194407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707f481ce3097ef1da3af9964bd36bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da1ddf59efd582614505be50e813af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6bfefa5b41faae17987876d570685d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5980a054af3e565d5d0511b14695aaf1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e861f148f57d5bcdd82cd1fec3d594.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a3d8f7ee39ac3245c840a40f8af63d.png)
您最近一年使用:0次
2024-01-24更新
|
360次组卷
|
2卷引用:四川省泸州市泸县第四中学2023-2024学年高一下学期开学考试数学试题
名校
解题方法
3 . 设
是定义在
上的奇函数,且对任意实数
,恒有
.当
时,
.
(1)当
时,求
的解析式;
(2)计算
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d78dec1c1e00ec02d7bdaf76ef8901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3262781afb71e9dffc0b7fa1fe280cb2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad814089e37543b2f547af9ae75b6dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e259fe30c60fbee6f0a20574bc925d.png)
您最近一年使用:0次
2023-09-08更新
|
478次组卷
|
3卷引用:陕西省安康市2023-2024学年高二上学期开学摸底考试数学试题
陕西省安康市2023-2024学年高二上学期开学摸底考试数学试题(已下线)难关必刷02 函数的性质及应用-【满分全攻略】(人教A版2019必修第一册)山东省菏泽市郓城县第一中学(英华校区)2024届高三上学期9月月考数学试题
4 . 已知x为实数,用
表示不超过x的最大整数.例如
,
,
.若对于函数
,存在实数
且
,使得
,则称函数
是
函数.
(1)直接写出下列式子的值:
;
;
;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51d08d325c91669d7dd07d8642c217f.png)
(2)分别判断函数
,
是否是
函数;(只需写出结论)
(3)已知
,请写出一个a的值,使得
是
函数,并给出证明;
(4)定义:对于函数
,如果存在一个不为零的常数T,使得当x取定义域内的每一个值时,
都成立,那么就把
叫做周期函数 ,不为零的常数T叫做这个函数的周期 .如果在所有的周期中存在一个最小的正数,就把它叫做
的最小正周期 .设函数
是定义在R上的周期函数.其最小正周期为T,若
不是
函数.求T的最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe1e778c9e668594c42b77459328c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf813e9500eebd474511b865b876ea4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ae4ee70c548e841fd7ceeac3250b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8509800d6fa7569c2e296618e8f38d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19ec960e7b486de3916696346501a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(1)直接写出下列式子的值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841778fac3981dcf7a01a824e10e81a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a3c6125742fa147420517b099db105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbce20399f4a7df88f26b7718b90ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51d08d325c91669d7dd07d8642c217f.png)
(2)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519192532883d560482ad071e7b54c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce786a098b8bc5acec47cdb0fabee22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982786864f37e6f954e8d70f9970620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(4)定义:对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7c7b4934410a1727fe7024a6bd740f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
您最近一年使用:0次
名校
5 . 已知
是定义在
上的奇函数,且
,当
时,
.
(1)当
时,求
的解析式;
(2)求函数
在
上的零点构成的集合.
![](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/43c366c5c3f59a0ad981cb71e4d381e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a7a3641b3b1a6cfa4396f2af9fd94c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9c3cab0d7e6f7daa8deeb8ed7fdabb.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db32fe50bce282fba86d2ac54bdb33b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25a4b68d7be63ec223f642976a1087ba.png)
您最近一年使用:0次
2020-08-19更新
|
777次组卷
|
5卷引用:辽宁省沈阳市东北育才学校2021-2022学年高一下学期期初测试数学试题
辽宁省沈阳市东北育才学校2021-2022学年高一下学期期初测试数学试题江苏省常州市教育学会2019-2020学年高一上学期期末数学试题(已下线)对点练16 函数与方程-2020-2021年新高考高中数学一轮复习对点练(已下线)第04章+指数函数与对数函数(A卷基础篇)-2020-2021学年高一数学必修第一册同步单元AB卷(新教材人教A版)(已下线)第四章 指数函数与对数函数章节测试(A)-《聚能闯关》2021-2022学年高一数学提优闯关训练(人教A版2019必修第一册)
名校
6 . 已知
为实数,用
表示不超过
的最大整数,例如
,
,
.对于函数
,若存在
且
,使得
,则称函数
是“和谐”函数.
(1)判断函数
,
是否是“和谐”函数;(只需写出结论)
(2)设函数
是定义在
上的周期函数,其最小周期为
,若
不是“和谐”函数,求
的最小值.
(3)若函数
是“和谐”函数,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe1e778c9e668594c42b77459328c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf813e9500eebd474511b865b876ea4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ae4ee70c548e841fd7ceeac3250b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f929c50f8ccc07ba58a4c34bb05d2bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19ec960e7b486de3916696346501a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b551072bee20e351f14d362a3f0e5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47431a4b13e3ea3cba79a85fd77eabc2.png)
(2)设函数
![](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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982786864f37e6f954e8d70f9970620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-02-14更新
|
869次组卷
|
3卷引用:2020届北京市陈经纶中学高三上学期8月开学数学试题
11-12高三上·山东济南·阶段练习
名校
解题方法
7 . 已知定义在实数集
上的奇函数
有最小正周期2,且当
时,
.
(Ⅰ)求函数
在
上的解析式;
(Ⅱ)判断
在
上的单调性;
(Ⅲ)当
取何值时,方程
在
上有实数解?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba4fd0990bf06bb09edf1d946be657e.png)
(Ⅰ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
(Ⅱ)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7d09233dda337cccf16b2a47f8fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
您最近一年使用:0次