名校
解题方法
1 . 已知
是定义在
上的函数,如果存在常数
,使得对区间
的任意划分:
,都有
成立,则称
是
上的“绝对差有界函数”.
(1)分别判断
,
是否是
上的“绝对差有界函数”,若是“绝对差有界函数”,直接写出
的最小值(不需证明);若不是“绝对差有界函数”,直接写出函数的值域(不需证明);
(2)对定义在
上的
,若存在常数
,使得对任意的
,都有
,求证:
是
上的“绝对差有界函数”;
(3)设
是
上的“绝对差有界函数”,满足
,
,且对任意的
,都有
,求实数
的取值范围.
![](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/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804319e6cb58f07ee82ee364e334f36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cddd157e5a81d11a17daeae7882b85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee02fa2349fe9b9dd17c11665352c06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a552e0f8ccb78f2eec126ba95d8c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)对定义在
![](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/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f20b947d584a1dc48676c2ae6e2af52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ecdccf4a334ea959a456533c40d53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ac1c23f2a39df0652588ce63221df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd80e859f2a7935d7d621e202422621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
2 . 若函数
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150583385e069735493bfe52da78711a.png)
A.定义域为![]() | B.值域为![]() |
C.图象过定点![]() | D.在定义域上单调递增 |
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3 . 已知函数
的定义域为集合
,值域为集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3f02900d098c6afa48d589eb920a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b98b1fdd7643c5a8d01088daf369af2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024高三·全国·专题练习
名校
解题方法
4 . 若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ba4d2fc9280cbc9c8b94ac031584f2.png)
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ba4d2fc9280cbc9c8b94ac031584f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86647b813d55593f0df2546940c227ca.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024高三·全国·专题练习
5 . 已知函数
,则函数
的值域为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d83271ac485ee8693d0ebae9a602dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4547821a5338114211c160cced1e4d0b.png)
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解题方法
6 . 已知函数
和
的定义域分别为
和
,若对任意
,恰好存在
个不同的实数
,使得
(其中
),则称
为
的“
重覆盖函数”.
(1)判断
是否为
的“n重覆盖函数”,如果是,求出
的值;如果不是,说明理由.
(2)若
,为
,的“2重覆盖函数”,求实数
的取值范围;
(3)函数
表示不超过
的最大整数,如
.若
为
的“
重覆盖函数”请直接写出正实数
的取值范围(无需解答过程).
![](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/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eddf991be37d25d033f78bd3511809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d5df7922a4e98e8e07bf418dd48a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44a5aed663a9b61ef7355b38c77d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d1a18f254577a0ce74ceb27364b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17efb86d82b9ddf50af4c23632a05c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e60e9c1e65686f8cd28a28abb8282c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f246e5b05b68bb9fdeb12a319aa7136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa88c20e58953bba4ed04d3ce419df95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)函数
![](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/240ca781ffd5d55cc9b7dd551879ce65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4987dca9120f6a58139fd3e412ed77c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a899e901b141a0a6d56e3387ecf9f047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e946baf1316ac1f219398ecedadf6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-06更新
|
255次组卷
|
3卷引用:浙江省临平萧山联考2023-2024学年高二上学期期末数学试题
名校
解题方法
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df8e9dda6f89d7c16c02d8dacf7461.png)
(1)当
时,求该函数的值域;
(2)若
对于
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df8e9dda6f89d7c16c02d8dacf7461.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66ef59c3970f3581a5ea29e21fd564d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd303ea196ae03b9c08459ad1f2f30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f3fc2a6b50f762c8378283b56023f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
8 . 已知函数
是奇函数.
(1)求
的值和函数
在区间
上的值域;
(2)若不等式
对于任意的
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b42a38b47ae296f3c8f3a77201497d.png)
(1)求
![](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/74440ee5b3fe9565f3cb09ac36998096.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14b8554de5184865801439d0d81bed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b12f2ff24c52fded1dfd0f0b6940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-02-06更新
|
312次组卷
|
2卷引用:湖南省长沙麓山国际实验学校2023-2024学年高二4月学情检测数学试题
名校
9 . 函数
的值域是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206c9e393ab54f209169bcdb5b81b3ed.png)
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解题方法
10 . 已知x满足
.
(1)求
的取值范围;
(2)求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbae29834c59537e73448575734123bf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6abfcf991e757a5057a5dbe55c967e.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5f18634277ba10e64a7f38a4445f9f.png)
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2023-12-26更新
|
393次组卷
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4卷引用:江西省宜春市宜丰中学2023-2024学年高二上学期1月期末考试数学试题
江西省宜春市宜丰中学2023-2024学年高二上学期1月期末考试数学试题河南省洛阳市强基联盟2023-2024学年高一上学期12月联考数学试题陕西省宝鸡市实验高级中学2023-2024学年高一上学期阶段检测(四)数学试题(已下线)专题16对数函数-【倍速学习法】(人教A版2019必修第一册)