名校
1 . 给出函数
,
(1)若
,求不等式
的解集;
(2)若
,且
,求
的取值范围;
(3)若
,非零实数
,
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f18cf2aa76c59569a668ee8fb5ae420.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62acc97e485075f489e1d5e96e09958.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/867f0794e209c2aa6dc1ded523427ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3c5462af41f417a830b88fbad13bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e1d71a91451f7086d9237c0fea607e.png)
您最近一年使用:0次
名校
2 . 已知
,函数
,
.
(1)若
,
,求
;
(2)若
,
,求
;
(3)若
,
,问:
是否为定值(与a无关)?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a93f4b5daefd7fc2f0ee661400357a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5024c44449abcba05cd24bf1dddd4e63.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73b85378c1f65d0ca0e4c30a14ccee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302b4d220b829aeede0b874ac26c35f7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054685034d95079ee155203401e494f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15eac3345475bb6a21a5d3f5db76b1dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51d3fb60fdba2bc8bd0811fcabfa3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82f4ce319a1e1ff7137e0267201ea27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
您最近一年使用:0次
2023-07-25更新
|
549次组卷
|
3卷引用:江苏省徐州市等3地2022-2023学年高一上学期期末数学试题
解题方法
3 . 已知函数
,
.
(1)求
的值;
(2)从下列问题中选1个作答.
①
,定义
,求
的解析式并写出
的最小值;
②
,定义
,求
的解析式并写出
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce427e97019745d570dd2728027fba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ded73c42d7ae61aa89c42d6fb219d832.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ba04d4e21dce4a5a0149e1918d01632.png)
(2)从下列问题中选1个作答.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6081690f4c0352290b2e88689b4945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478e75f2162f25b93d4c337e2829fc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7225c625819b7bfeb393a377ec2d74a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6081690f4c0352290b2e88689b4945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9e0f7fd210c8ebc45692f5be03db7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f0f54dd104b99379c9953c429acf5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
2023高三·全国·专题练习
解题方法
4 . 某地区2020年底有居民住房面积为a,现在居民住房划分为三类,其中危旧住房占
,新型住房占
.为加快住房建设,计划用10年的时间全部拆除危旧住房(每年拆除的数量相同),自2021年起居民住房只建设新型住房.从2021年开始每年年底的新型住房面积都比上一年底增加
,用
表示第n年底(2021年为第一年)该地区的居民住房总面积.
(1)分别写出
,
,
的计算公式并归纳出
的计算公式(不必证明).
(2)危旧住房全部拆除后,至少再过多少年才能使该地区居民住房总面积翻两番?(精确到年,
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ee628efd6b2f7296c106dd5cbae42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)分别写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)危旧住房全部拆除后,至少再过多少年才能使该地区居民住房总面积翻两番?(精确到年,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f4d8318aba2dd01bfdc4c6b77c6121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab1cb23df1e01a5120207dbfb4ae6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845c6f77c2e365072e40286e6002d677.png)
您最近一年使用:0次
名校
5 . 已知函数
,
.
(1)若函数
在
内有唯一零点,求a的取值范围.
(2)设函数
的最大值、最小值分别为M,m,记
.设
,函数
,当
,
时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5a8a2c5eb1378820b13b3ac89fa95c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49200638dacabba433c89091a85a3a89.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47b28cc54ced61f5ab8d310dc76a982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6dd738ca111f49063b03cbb959a451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31a53fafc6c5d5e13ac3eab08f997b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a870bbc137db5ec904afd026c5681bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e212491cebea5ab07e1ee7f2b4e7d2fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd93b77cc67780afe79261829df669c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
您最近一年使用:0次
2023-06-03更新
|
326次组卷
|
4卷引用:四川省眉山市彭山区第一中学2022-2023学年高一下学期5月月考数学试题
四川省眉山市彭山区第一中学2022-2023学年高一下学期5月月考数学试题湖南省衡阳市第一中学2022-2023学年高一下学期期末数学试题河南省部分重点中学2023-2024学年高一上学期12月质量检测数学试题(已下线)湖南省名校2023-2024学年高一上学期12月联考数学试题
名校
解题方法
6 . 已知两个变量
且
满足关系式
,且
是
的函数.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/18/fb160dbb-e69a-4e91-ba11-b9b90fbd9f18.png?resizew=168)
(1)写出该函数的表达式
,值域和单调区间(不必证明);
(2)在坐标系中画出该函数的图象(直接作图,不必写过程及理由).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656d649176f38261805ad14bb1066216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a0e656a2de8d47b9001cc32b1316eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6b3feb5aad6b9d53cb432532681d27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/18/fb160dbb-e69a-4e91-ba11-b9b90fbd9f18.png?resizew=168)
(1)写出该函数的表达式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)在坐标系中画出该函数的图象(直接作图,不必写过程及理由).
您最近一年使用:0次
名校
解题方法
7 . 某公司为了提升销售利润,准备制定一个激励销售人员的奖励方案.公司规定奖励方案中的总奖金额y(单位:万元)是销售利润x(单位:万元)的函数,并且满足如下条件:①图象接近图示;②销售利润x为0万元时,总奖金y为0万元;③销售利润x为30万元时,总奖金y为3万元.现有以下三个函数模型供公司选择:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/0895f914-d3d0-4575-aa54-d3e148c59d52.png?resizew=129)
A.
;B.
;C.
.
(1)请你帮助该公司从中选择一个最合适的函数模型,并说明理由;
(2)根据你在(1)中选择的函数模型,解决如下问题:
①如果总奖金不少于9万元,则至少应完成销售利润多少万元?
②总奖金能否超过销售利润的五分之一?
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/0895f914-d3d0-4575-aa54-d3e148c59d52.png?resizew=129)
A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be21cea6c1184ff324e8968511b39f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c8e1d0fa3a79fbf1f1b900e8376728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f29a5639dadf19be04cb97b70165c27b.png)
(1)请你帮助该公司从中选择一个最合适的函数模型,并说明理由;
(2)根据你在(1)中选择的函数模型,解决如下问题:
①如果总奖金不少于9万元,则至少应完成销售利润多少万元?
②总奖金能否超过销售利润的五分之一?
您最近一年使用:0次
2023-01-11更新
|
1065次组卷
|
7卷引用:江苏省苏州市2022-2023学年高一上学期期末学业质量阳光指标调研数学试题
解题方法
8 . 已知函数
的表达式为
,对于任何实数x,
都有意义,求
的范围并判断
所在的象限.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5661318fff6d93df23a4c809528e184f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
,
,若对任意的x,y都有
.
(1)求
的解析式;
(2)设
,
(ⅰ)判断并证明
的奇偶性;
(ⅱ)解不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17afd02a58c3d3c25ac4f8cab171e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac829d3069cf983b89b67c73544c8baf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c15203cc22f37937619bc22b880f407.png)
(ⅰ)判断并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(ⅱ)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c954734b0cb6212c0e185cd910bb7338.png)
您最近一年使用:0次
2022-12-17更新
|
340次组卷
|
2卷引用:陕西省西北工业大学附属中学2022-2023学年高一上学期第二次月考数学试题
名校
解题方法
10 . 设a为实数,给定区间I,对于函数
满足性质P:存在
,使得
成立.记集合
.
(1)设
,
,求证:
;
(2)设
,
,若
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c85eadf1c23b6b46183e978071442a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8af703255327c297eb54bfe318452b9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dfa9363036589c4e93868fe0437a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec84404bbf6cf4a9d992e1760dcfdd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cac663990f61a4a3086c6bea3d51f9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/688afe078f708dcdec80f68a1386c041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f412e27806d298e08c365ee16b00f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e74920f57028200604c2691c8f0fb89.png)
您最近一年使用:0次