名校
解题方法
1 . 已知函数
为定义在
上的奇函数.
(1)求实数b的值;
(2)当
时,用单调性定义判断函数
在区间
上的单调性;
(3)当
时,设
,若对任意的
,总存在
,使得
成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c8d98ee11235b9ff6c47a5ab20b99c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求实数b的值;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb8b52b9f71d8cc6e86c7d9a8a47a16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7192c7ee3cec2f724ee10e3bd4d4002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a49684ba67f71171321586f1a77ad4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160eed42a1bf26ff6193cbd9fb311340.png)
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2023-12-04更新
|
410次组卷
|
2卷引用:山东省青岛第二中学2023-2024学年高一上学期期中考试数学试卷
名校
解题方法
2 . 山东省青岛第二中学始建于1925年,悠悠历史翻开新篇:2025年,青岛二中将迎来百年校庆.在2023年11月8日立冬这天,二中学子摩拳擦掌,开始阶段性考试.若
是定义在
上的奇函数,对于任意给定的不等正实数
,不等式
恒成立,且
,设
为“立冬函数”,则满足“立冬函数”
的x的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a271c3a5d9880c1b15b581dac2c166a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f003178e540e09aebb952c33a3a685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c45b699cedb3c1868e77f224603227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0879734ee766cb630cfeb3f25fea7d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
3 . 若
是定义在
上的偶函数,当
时,
.
(1)求
的解析式;
(2)讨论
在
上的单调性,并用定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d028846b8614318fbf90387d13c75b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4544c8626f01deff908469a90504b2c7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
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解题方法
4 . 已知
是定义在
上的奇函数,当
时,
.
(1)求
在
上的解析式;
(2)根据函数单调性的定义,证明
在区间
上单调递减.
![](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/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde0229bf44aebcdce4f61d9b05df30d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(2)根据函数单调性的定义,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879234adbae93aa72b7e101b3738d4e0.png)
您最近一年使用:0次
5 . 德国数学家康托尔是集合论的创立者,为现代数学的发展作出了重要贡献.某数学小组类比拓扑学中的康托尔三等分集,定义了区间
上的函数
,且满足:①任意
,
;②
;③
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b39bbfd4894f4d2ca18473a3e42f82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ee7abd882ba99660bca68ebf544cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7f3dbe1155bef98639f30a7d24f304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfca9e2cea383880fb2dfe0e71b9e2b.png)
A.![]() ![]() | B.![]() ![]() |
C.当![]() ![]() | D.当![]() ![]() |
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2023-11-29更新
|
215次组卷
|
2卷引用:山东省烟台市2023-2024学年高一上学期期中数学试题
名校
6 . 已知函数
为奇函数.
(1)求实数
的值;
(2)判断
在
上的单调性,并用定义证明;
(3)若对于任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc25c261cfb3d8134f1681aedb3a52f.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd67623d65571ec957c41057a3182a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-11-28更新
|
850次组卷
|
5卷引用:山东省普高大联考2023-2024学年高一上学期11月期中联合质量测评数学试卷
名校
7 . 函数
定义域为
,对任意的
都有
,则称函数
为“
函数”,已知函数
是“
函数”,则关于
的不等式
的解集为( )
![](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/6c4b86ce635dbd53ce824a7c93cd23fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2bfd103090863fbcc1bd10618cff0c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c951871f047891cea9434bd220a201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3ca700dbdfefffcc21eb9eb9dc22a8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
8 . 已知函数
是偶函数,当
时,
恒成立,设
,
,
,则a,b,c的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5220a5c9271c80b38c5d4a41c523f776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b6fbd08afa059e0fd6196f6a5b8c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1906b9f4e7fcb125639520ebf0c094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17b9ba72a83a45d274fb0c14043e70a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d193f345c773ff0a024ecfedcd3fdd4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 已知函数
,
满足
.
(1)设
,求证:函数
在区间
上为减函数,在区间
上为增函数;
(2)设
.
①当
时,求
的最小值;
②若对任意实数
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d0fa6692dabe155895e6deca98da84.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4a90cfdbfa05577b6ec0b22739e7c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95167d339851668666c00819537737c4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56251c77cc3fd1db89c33003519a116.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5db0c90f213d6bf3ef7949cc00aa27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a37e21a940c03985a1458167b5e6c24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-11-27更新
|
401次组卷
|
5卷引用:山东省潍坊市2023-2024学年高一上学期11月期中质量监测数学试题
山东省潍坊市2023-2024学年高一上学期11月期中质量监测数学试题山东省淄博市美达菲双语高级中学2023-2024学年高一上学期期中数学试题湖北省黄冈市浠水县第一中学2023-2024学年高一上学期期中数学试题江西省抚州市资溪县第一中学2023-2024学年高一上学期期中调研数学试题(已下线)专题04 函数的性质与应用1-期末复习重难培优与单元检测(人教A版2019)
名校
解题方法
10 . 已知定义在
上的函数
是奇函数,且
时
,则下列叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.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/5bbb66cea9934320b6bb723dc7b1a076.png)
A.当![]() ![]() |
B.![]() |
C.![]() ![]() |
D.函数![]() ![]() ![]() |
您最近一年使用:0次
2023-11-26更新
|
491次组卷
|
6卷引用:山东省临沂第十八中学2023-2024学年高一上学期第三次月考考前模拟数学试题