1 . 偶函数
在
的解析式为
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d581aceee8a28d01addb3621ee084b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14be574d4eaf7f7e0d2b28ade7f3ea1.png)
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解题方法
2 . 德国数学家狄利克雷在数学领域成就显著,以其名命名函数
,该函数被称为狄利克雷函数,关于狄利克雷函数有如下四个命题:
①
;②对任意
,恒有
成立;
③任取一个不为零的有理数
,
对任意实数
均成立;
④存在三个点
,
,
,使得
为等边三角形;
其中正确的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d47d46bba886a995274646ffb19ae3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7298e41399f66a12e2dad0a716106b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c660c78aa2f9fc7efe6e35e92c2ea024.png)
③任取一个不为零的有理数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a9c3e804fc20446ad72da8339c20ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
④存在三个点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd9e756e1da0ae9beed0c9c117b74178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee173145668f082751c6e9d629e8cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836e5321ec22c9840a195bc146861cee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
其中正确的序号为( )
A.①②③ | B.②③④ | C.②④ | D.①②③ |
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名校
解题方法
3 . 已知函数
的定义域为
,若存在常数
,使得对任意的
,都有
,则称函数
具有性质![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
(1)若函数
具有性质
,求:
的值;
(2)设
,求证:存在常数
,使得
具有性质
;
(3)若函数
具有性质
,且
的图像是一条连续不断的曲线,求证:函数
在
存在零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094f977194228bed828f3507f5898934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d66abb9d5cb6212adcd4869871581cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41b85f6960a2a4f988e5ddd9ef48d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1d50578658f71442034e0e04f804de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae38cfa3259536009ae02d160450704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094f977194228bed828f3507f5898934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd2c5760181b2c974811564b55b65f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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4 . 函数
的定义域是__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce855dd8863cd9cb61a88d9b928e7a3.png)
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名校
5 . 已知函数
的表达式为
,若方程
有四个不相等的实根
,且
,则
取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664d5a568352ae5c7bb21549055ecd7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e3397839f4b65912c2f0cfe7f05eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd42c34b2f926f4600e8622b961e3c92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4077511e2a6cd8caff76581a94b6fe.png)
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2024-01-15更新
|
219次组卷
|
2卷引用:上海市松江区2023-2024学年高一上学期期末质量监控数学试卷
名校
解题方法
6 . 某机构为了研究某种药物对某种疾病的治疗效果,准备利用小白鼠进行试验,研究发现,药物在血液内的浓度与时间的关系因使用方式的不同而不同:若使用注射方式给药,则在注射后的4小时内,药物在白鼠血液内的浓度
(单位:毫克/升)与时间
(单位:小时)满足关系式
(
,
为常数);若使用口服方式给药,则药物在白鼠血液内的浓度
(单位:毫克/升)与时间
(单位:小时)满足关系式
,现对小白鼠同时进行注射和口服该种药物,同时使用两种方式给药后,小白鼠血液中药物的浓度等于单独使用每种方式给药的浓度之和.
(1)若
,求4小时内,该小白鼠何时血液中药物的浓度最高,并求出最大值;
(2)若小白鼠在用药后4小时内血液中的药物浓度都不低于6毫克/升,求正数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d071c4bf949631450d711ee6ced17c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9987c1a6fd1f1c8f3c7bebb3da5f1a8c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)若小白鼠在用药后4小时内血液中的药物浓度都不低于6毫克/升,求正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
7 . 已知条件
:
,条件
:
,命题A:若
成立,则
成立.若命题
是真命题,则实数
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf670b5877216880febf2a19cb90e80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd6912849c58f0f51e55ab8b80b909c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
8 . 已知全集为
,集合
,函数
的定义域为集合
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c400ea671bd1cfbf4dc6a155321c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9493f278590f8c36489d0f0ee7a1e8e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fd1ee756ac1b0f950c0f6a2bce3178.png)
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9 . 已知
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5215a578933ba72022450a6d3a37d14.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd81c4d53f2c07d81de21a9871200e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40747e10c4b1af1f0dcd4ba16e1327f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5215a578933ba72022450a6d3a37d14.png)
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10 . (1)
是定义在正整数集上的函数,并且满足
①当
为正整数时,
;
②当
为非负整数时,
.
求
的值.
(2)函数
定义在有序正整数对的集合上,且满足下列性质:
①
;②
;③
.
求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f6c12705300de947fc04865b2747cd9.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6360d35614281c3a6b08179ef77cc4c.png)
求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495955d39b954d26852f3f58c9df0a03.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e21e386e8449fe122efe8789ab77e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217758c83175763d7d3c306d12c22176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e67dd773c99cf71254097f7a838ae7a0.png)
求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30547752a04f8877c99a1084c6e145e3.png)
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