1 . 已知函数
.
(1)设
的反函数为
,求
的最值.
(2)函数
满足
,求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edb40aa0c70fcef722fdb19ff134b48.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90459228092aec6d324784babcbb2cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92860378096f519a8fb276d07dbfabce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7d4a1283e55b1dc8d63fa012c53af3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7511e6ce72a5232820b7007f976be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee284116732bcc5309e44ca41abdcfa.png)
您最近一年使用:0次
名校
2 . 立德中学高一数学兴趣小组利用每周五开展课外探究拓展活动,在最近的一次活动中,他们定义一种新运算“
”:
,
,通过进一步探究,发现该运算有许多优美的性质:如
,
等等.
(1)对任意实数
,请判断
是否成立?若成立请证明,若不成立,请举反例说明;
(2)已知函数
,函数
,若对任意的
,存在
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5060d9b229d6cfc8b21ecb5549d17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347604752750649bde7b37c456c8263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c46a883a70c6ca89d9877ed4894bc5.png)
(1)对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee069136ee60c3983c957ba0961f912.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6051ffc0e9ae07f6dd5e8a825c02b97b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103d9319c355a06e10c118088dac5991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12965bbc260bdbb0df0a110e59fb8d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5987e76a34012a8bd0d51da0fddd83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-02-02更新
|
254次组卷
|
2卷引用:上海市金山中学2021-2022学年高一下学期3月月考数学试题
解题方法
3 . 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)
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22-23高一上·上海浦东新·阶段练习
名校
4 . 已知
的定义域为
,且满足下列三个条件:①
在
上为严格增函数;②
;③对任何实数
,都有
.
(1)求
的值;
(2)从对称中心和对称轴两方面讨论
的对称性,如果具有对称性,请写出一个对称中心、一条对称轴,并给出证明;如果没有对称性,请说明理由.
(3)解不等式:
.
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed670b1f668778c6243f3f7470ee7d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d542cc432e36fcc317f799c5c81e67b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5890df42eb7838a47ae1625f011b51.png)
(2)从对称中心和对称轴两方面讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
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解题方法
5 . 在数学中,双曲函数是与三角函数类似的函数,最基本的双曲函数是双曲正弦函数与双曲余弦函数,其中双曲正弦:
,双曲余弦函数:
,(
是自然对数的底数).
(1)解方程:
;
(2)写出双曲正弦与两角和的正弦公式类似的展开式:
________,并证明;
(3)无穷数列
,
,
,是否存在实数
,使得
?若存在,求出
的值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea54f9abcfb83c1f8d4860de58d9a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cea2c942a40975a4bed91960a217cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/507ea92ca0fbfa95da0f01c201ff54a4.png)
(2)写出双曲正弦与两角和的正弦公式类似的展开式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6343611e15d5f379d06115077f05d2a4.png)
(3)无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecf3a1fecf89a37a677393d0bfe27b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7268804f4cde744cf387b933409d0c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 已知函数
的定义域为
,给出以下两个结论:
① 若函数②的图像是轴对称图形,则函数
的图像是轴对称图形;
② 若函数
的图像是中心对称图形,则函数
的图像是中心对称图形.它们的成立情况是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
① 若函数②的图像是轴对称图形,则函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add1a06062f9196e8e83452269db2316.png)
② 若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add1a06062f9196e8e83452269db2316.png)
A.①成立,②不成立 | B.①不成立,②成立 |
C.①②均不成立 | D.①②均成立 |
您最近一年使用:0次
2021-05-05更新
|
300次组卷
|
6卷引用:课时13 函数的基本性质-2022年高考数学一轮复习小题多维练(上海专用)
(已下线)课时13 函数的基本性质-2022年高考数学一轮复习小题多维练(上海专用)(已下线)考向03 函数及其性质-备战2022年高考数学一轮复习考点微专题(上海专用)上海市青浦区2021届高三二模数学试题(已下线)第04讲 函数最值与性质-3(已下线)专题03 函数的概念与性质(模拟练)-2(已下线)专题3.2 函数的基本性质-《讲亮点》2021-2022学年高一数学新教材同步配套讲练(人教A版2019必修第一册)
7 . 设函数
(
),若函数
的零点为4,则使得
成立的整数
的个数为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504cd3f2ef8ae4b46e2b6cbb823f519b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4b443a18d8be7508622cddd5c4fd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00055e2f9b92c631ed0e063e8464a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
8 . 已知
.
(1)当
时,讨论函数
的奇偶性;
(2)当
,
,
时,
的最大值为
,求
的零点;
(3)当
时,对于任意的
,总有
,试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adebd26bdc1c9f97d05f111fb22b1073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0204d26772210e7d5d781bb173946c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c6b9fa72109ba69163a5c6b7874a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69303621c56f67b4ec4e0ac575deb554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b22587c4fcd78f4b64296e9a1116fccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ab85c075a09d55d69e159e4abb268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0204d26772210e7d5d781bb173946c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f318d8fab196afb5be036094231e5f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df041da59fbbfd11c5c1dd3d72813247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021·上海浦东新·三模
名校
解题方法
9 . 设D是
的一个子集,称函数
为“机智”的,若存在奇函数
,使得
,有两个命题:①若对任意
,都成立
,
,则
是“机智”的;②若对任意
,都成立
,则
是“机智”的;则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2ab09ce6ffc17ccbe9d4b203009d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf4ede15273e054f093e34d326fbefc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c2f06ee2e2fde6df5b54e7bb535f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3445ba0f5a64bd73250faa3dd1c6e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f662024fea739a9cfdfd55ae9a107ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3445ba0f5a64bd73250faa3dd1c6e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
A.①是真命题,②是假命题 |
B.①是假命题,②是真命题 |
C.①、②都是假命题 |
D.①、②都是真命题 |
您最近一年使用:0次
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解题方法
10 . 已知
、
是定义在
上的函数,且
在
上是严格增函数,设
满足
,且对于
中的任意两个相异的实数
、
,恒有
.
(1)求证:
在
上是严格增函数;
(2)设
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548636534994cd465dfc7bf7dd41505b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a301678a22fd9ebedb6c142a5a73bb4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.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/2407042c0e07f46e7f0cc703aa37e2d8.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43fb7af688c7d890a2221ab00eee4e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2408a1f2c35f6277efa4f8e58e93fc0.png)
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