名校
解题方法
1 . 已知函数
.
(1)若
满足
为R上奇函数且
为R上偶函数,求
的值;
(2)若函数
满足
对
恒成立,函数
,求证:函数
是周期函数,并写出
的一个正周期;
(3)对于函数
,
,若
对
恒成立,则称函数
是“广义周期函数”,
是其一个广义周期,若二次函数
的广义周期为
(
不恒成立),试利用广义周期函数定义证明:对任意的
,
,
成立的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17422461d5ec2bff93452619c6b774f3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b727eb9da56be079445321cf61cf26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be344d1925b25e44f3f8b34d2c193ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b186e49220460b09f85519aa657527b.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf03e1296f7f5bb315c87893caee079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4056806dc4a2f28e267f879b6f5c0079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c204be088a8fc6c096eedd5b1e7dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(3)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06d64b48da95b74aa5e12bc5da127dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c90d0f5f17344c0eb75c2aea394bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183ba00d69af06d9a950469b38cfe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a35277c37144276ead40bb74a51481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183ba00d69af06d9a950469b38cfe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb05fd7662d05b9e2051b044de722840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05dd02b6f561dcf94bab8a3160108d5.png)
您最近一年使用:0次
2020-08-25更新
|
1053次组卷
|
6卷引用:2019年上海市建平中学高三三模数学试题
2019年上海市建平中学高三三模数学试题(已下线)专题2.3 函数的奇偶性与周期性(精讲)-2021年高考数学(理)一轮复习学与练(已下线)专题2.3 函数的奇偶性与周期性(精讲)-2021届高考数学(理)一轮复习讲练测上海市建平中学2019届高三下学期5月月考数学试题(已下线)3.2函数的基本性质-2020-2021学年高一数学同步课堂帮帮帮(人教A版2019必修第一册)(已下线)专题03 函数的概念与性质(模拟练)-2
名校
解题方法
2 . 已知集合
.
(1)求证:函数
;
(2)某同学由(1)又发现
是周期函数且是偶函数,于是他得出两个命题:①集合
中的元素都是周期函数;②集合
中的元素都是偶函数,请对这两个命题给出判断,如果正确,请证明;如果不正确,请举出反例;
(3)设
为非零常数,求
的充要条件,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2041f5b087d5a81755d5d26c381ec22d.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd87e951d72ddcd358c5171219f1caf8.png)
(2)某同学由(1)又发现
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e174ad99b65cb6a865b5b4f7ccb030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2fbe843ce1c7880866e21789e9e1f70.png)
您最近一年使用:0次
名校
3 . 已知定义在
上的函数
满足以下三个条件:
①对任意实数
,都有
;
②
;
③
在区间
上为增函数.
(1)判断函数
的奇偶性,并加以证明;
(2)求证:
;
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf84c184be32752d1c14e6f23fecda8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6855784817151468771f29c0fc38fc9.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4cff510b81f7160ec53b7ef179f114.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
您最近一年使用:0次
2019-12-01更新
|
929次组卷
|
3卷引用:浙江省宁波市效实中学2019-2020学年高一上学期期中数学(理)试题
4 . 给出集合
.
(1)若
,求证:函数
;
(2)由(1)分析可知,
是周期函数且是奇函数,于是张三同学得出两个命
题:命题甲:集合
中的元素都是周期函数.命题乙:集合
中的元素都是奇函数. 请对此
给出判断,如果正确,请证明;如果不正确,请举反例;
(3)若
,数列
满足:
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
,数列
的前
项
和为
,试问是否存在实数
、
,使得任意的
,都有
成立,若
存在,求出
、
的取值范围,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2797a0dde20f22497c6190d08c71b741.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c6d8eccab2b897f45885ed81195248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5314a9d2205a2beba0dcffb8fd943b18.png)
(2)由(1)分析可知,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c6d8eccab2b897f45885ed81195248.png)
题:命题甲:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
给出判断,如果正确,请证明;如果不正确,请举反例;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96f3ea0467dc6393d7c4b602175a394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5fb8208a95205a6437385ba884547a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab958eede2dbad749ba70bb230c88fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5014429b696a37a9461b66f22b1800.png)
存在,求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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解题方法
5 . 若函数
的定义域为R,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aae4b2e40ca578ac5dbb8f07693dfff.png)
(1)求
的值,并证明函数
是偶函数;
(2)判断函数
是否为周期函数并说明理由,求出
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aae4b2e40ca578ac5dbb8f07693dfff.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baeef9267fa2d3de28e70839dc3db48e.png)
您最近一年使用:0次
名校
6 . 对于函数
,
,
,
及实数m,若存在
,
,使得
,则称函数
与
具有“m关联”性质.
(1)分别判断下列两组函数是否具有“2关联”性质,直接写出结论;
①
,
;
,
;
②
,
;
,
;
(2)若
与
具有“m关联”性质,求m的取值范围;
(3)已知
,
为定义在R上的奇函数,且满足:
①在
上,当且仅当
时,
取得最大值1;
②对任意
,有
.
求证:
与
不具有“4关联”性质.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02059edf02fba0e7c62b7c2a48ef1184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed7a0e7e7a3b49b4cd2e777a64e9061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4413796ac3d5ca067bf70334101f5440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3ac1b540727626af78788a8e5f15de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe6b84f7980bf119ee652fc253ed759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)分别判断下列两组函数是否具有“2关联”性质,直接写出结论;
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba296251f96be272abf30c1c0e1a8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699f767ccf837c2bf8019d03451849c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174550b7c81d8d41084dcafad90bfbe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a79d7f73b6128650bf7aed538260c72.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96101eb5dce02c0213ad008413f3066.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a78355986534b6e50bd7cabc9290a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18db64040b2fa9d65075b41ada928fa6.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9c839f85fe048ed0882889e22f5166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d2c5422d4b9f8c11a5ad1b62c6bb87.png)
您最近一年使用:0次
2023-06-19更新
|
341次组卷
|
3卷引用:北京市顺义区2022-2023学年高一下学期期中考试数学试题
名校
解题方法
7 . 定义在
上的非常值函数
、
,若对任意实数x、y,均有
,则称
为
的相关函数.
(1)判断
是否为
的相关函数,并说明理由;
(2)若
为
的相关函数,证明:
为奇函数;
(3)在(2)的条件下,如果
,
,当
时,
,且
对所有实数
均成立,求满足要求的最小正数
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23cd0a1f49a060640fa4981ba98fe0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa1c68cebf2203d277f61cfdbacf175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)在(2)的条件下,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc2b7be871fef904c94ef6360ee32bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8663f63173aa6f7646eea8f1053170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b94f151c00959a1cd3946e7f8405337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c717940255e8135ebff734c2b0e94722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7c7b4934410a1727fe7024a6bd740f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
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8 . 定义域为
的函数
,对于给定的非空集合
,
,若对于
中的任意元素
,都有
成立,则称函数
是“集合
上的
函数”.
(1)给定集合
,函数
是“集合
上的
函数”,求证:函数
是周期函数;
(2)给定集合
,
,若函数
是“集合
上的
函数”,求实数
、
、
所满足的条件;
(3)给定集合
,函数
是集合
上的
函数,求证:“
是周期函数”的充要条件是“
是常值函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc487556ec9fca7872e6fdbbe16136d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff5f184ffc037cb5dabfd32a03a6ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875be7d4b5aee30eea8c4ad8d862914a.png)
(1)给定集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265e81e52218232e16c78f57b3aa0de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875be7d4b5aee30eea8c4ad8d862914a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)给定集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f1431bca7e0baac283abc1974afe4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3dea43b478cd72cb419548c21fad67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875be7d4b5aee30eea8c4ad8d862914a.png)
![](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/071a7e733d466949ac935b4b8ee8d183.png)
(3)给定集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080550853fb08fc020f092e2e9b44843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875be7d4b5aee30eea8c4ad8d862914a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
您最近一年使用:0次
解题方法
9 . 已知函数
的定义域为
,若存在常数
和
,对任意的
,都有
成立,则称函数
为“拟线性函数”,其中数组
称为函数
的拟合系数.
(1)数组
是否是函数
的拟合系数?
(2)判断函数
是否是“拟线性函数”,并说明理由;
(3)若奇函数
在区间
上单调递增,且
的图像关于点
成中心对称(其中
为常数),证明:
是“拟线性函数”.
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9eb0abfebb7bb39204e9aa051aa7f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85899a6f573914e34170ea6b2e6b27cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109d7264547e05af38ef2f36ec31f6d4.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188074ba24ae37b38cc0c614a2274d88.png)
(3)若奇函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad7349dcd23527bce8da3e344459659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
名校
10 . 定义:若函数
的定义域为D,且存在非零常数
,对任意
,
恒成立,则称
为线周期函数,
为
的线周期.
(1)下列函数
(其中
表示不超过x的最大整数),是线周期函数的是____________(直接填写序号);
(2)若
为线周期函数,其线周期为
,求证:
为周期函数;
(3)若
为线周期函数,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85eabd57a1bc7fde8cd6da81977bca5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)下列函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5276150cf27c826686b5f9df818dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd182241405bd00367a423e61df292a5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05312d9a1821302e6fba94998ee431e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2021-03-24更新
|
812次组卷
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10卷引用:北京市海淀区2017-2018学年高一上学期期末考试数学试题
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