1 . 函数
满足
,
,
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a580cb582c782207eea3e1387cc627.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0f201ef91b07563cb830f20fc5cea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32447060a910faf370a7715ecf4c97e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a35707dd2ed993f63bccfa59dba978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b894b7836b2dd6c45d8224de34d2cda6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a580cb582c782207eea3e1387cc627.png)
您最近一年使用:0次
名校
解题方法
2 . 已知定义域为R的函数
满足:
,
,且
,则下列说法不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067fd5770e2e2d208af78f1d9930abf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d88f7b54e9a6fd1bfe72c30d2964c7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fa4321e39ec6744d791a0d2d2e1a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b055c2e5c0a96771f7466e015a113021.png)
A.![]() | B.![]() |
C.若![]() ![]() | D.![]() |
您最近一年使用:0次
2024-06-05更新
|
437次组卷
|
2卷引用:江西省重点中学协作体2024届高三第二次联考数学试卷
3 . 对于定义域为R的函数
,若存在常数
,使得
是以
为周期的周期函数,则称
为“正弦周期函数”,且称
为其“正弦周期”.
(1)判断函数
是否为“正弦周期函数”,并说明理由;
(2)已知
是定义在R上的严格增函数,值域为R,且
是以
为“正弦周期”的“正弦周期函数”,若
,且存在
,使得
,求
的值;
(3)已知
是以
为一个“正弦周期”的“正弦周期函数”,且存在
和
,使得对任意
,都有
,证明:
是周期函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094f977194228bed828f3507f5898934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37dd12a44398c1da043894287ed73951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a24462399b3f0a55f56ee64f2eace7.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a198d1e1aad38ac00efe0529e6598967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69362920a541bcf343c7e2b6745c9473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c456cf701f55723e8d8f6c06114d9155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c27720b9725aab9069e49693f4ebf1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1741f5326542c1e7960ffe9a495f2f18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
您最近一年使用:0次
4 . 若函数
满足以下三个条件,则称
为
函数.①定义域为
;②对任意
,
;③对任意正整数
,
,当
时,有
.若给定
函数
某几个函数值,在满足条件①②③的情况下,可能的
如果有
种,分别为
,
,
,
.
等于
,
,
,
的最大值.这样得到的
称为
的最大生成函数.
(1)若
为
函数,且
是在给定条件
,
下的
的最大生成函数,求
和
的值;
(2)若
为
函数,且满足
,求数列
的前10项和;
(3)若
为
函数,且
是在给定条件
,
下的
的最大生成函数,求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f63c9be8167a50ac3996e007b124df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f133fb6340a11e7ba0240ac0e19339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2c8fda00e52527ee1472293c011eab.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/8b7acae2f2543b05e3c5677bd755b136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12877ebeba622c766be60b77efea9eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406957a919b3f16fb095aa9a8b7e2dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42bf9afee931791911f748fd84d45f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b754b86e63e02f3faeebff9c18c7460b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0749e3eddfb6056f19812d7fa713b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ddc3eab5cedbd4cba439126a8d2ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43172b8f2f645afeada31271d6f2dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a788e92a6e3e5e721096e78cc112adf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f196f6236188084f3b2c9f2b68c05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f196f6236188084f3b2c9f2b68c05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b17b16fdf70d2a885f5ab346afd18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ecae1c7e6e0dbb211105b27a0319c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830acb3d191d323e9ea6e710c7de0061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1135b03537fa6527c9ba3f639f64474c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31c3e1c4206e9bed7dd3c63d842080d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46069372b8f2a59194dad5978e18445.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7002fdc43f0d600cb517470ac65144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41678e5c9b510a2a4b798a0be444eb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc095001df2e68af03d6ed197a8d4372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab050e103632618580d0ec8728b584a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
5 . 已知函数
的定义域为
,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da5fc50eecebe9a33076014e09fb8a54.png)
A.![]() | B.![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
6 . 已知函数
的定义域与值域均为
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe852afd1bfd32a18a58944e138c83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a8bcbee61f6d9a84302a8eb0bbc4c5.png)
A.![]() | B.函数![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
7 . 设定义在函数
满足下列条件:
①对于,总有
,且
,
;
②对于,若
,则
.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8070c099832d3f7e6c0b5a7abafd2.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6101294ff728fdef676a5786590908.png)
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解题方法
8 . 已知
,
都是定义在
上的函数,对任意
,
满足
,且
,则下列说法正确的是( )
![](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/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109b8acf40088f0385734c68f7b2747f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45233ea15d19b08a43ad016a4f56e49e.png)
A.![]() | B.若![]() ![]() |
C.函数![]() ![]() | D.![]() |
您最近一年使用:0次
解题方法
9 . 已知定义在
上的函数
满足
,当
,时,
.下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2828d7e8b93a9f3e43181d74949dae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813b9aa31af28f99d21fc0dc0c95475c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f21febe8749e5e598124c2f6bb4025.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
2024-03-08更新
|
593次组卷
|
2卷引用:广东省2024届高三下学期开学考试数学试题
2024·全国·模拟预测
名校
解题方法
10 . 设
,
都是定义在
上的奇函数,且
为单调函数,
,若对任意
有
(a为常数),
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3612deddce866547aed0b67c6eb865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aedc1c8a16e306bcd6e5154f9ed6dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb821d2bd8c6ba7a244c3d918723cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271512f578a43c24c3e2c086fb14e0d2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-01-18更新
|
1659次组卷
|
6卷引用:2024届数学新高考学科基地秘卷(七)
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