1 . 解不等式组:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2ad7639ecabc7319fd20e1695b9def.png)
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2019-01-15更新
|
505次组卷
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2卷引用:【区级联考】上海市长宁区2017-2018学年高一(上)期末数学试题
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解题方法
2 . 函数
的定义域为
,函数
.
(1)求
的值;
(2)若
在
上为严格增函数,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abf44e3b1890581dcfd2dde5e5bd9ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f6ad85072c47fbb57fb296d4096322c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5b3fdd67091b72df5f1ce1d71b6c3f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5946299ed8f8c741a82c8d920e1e206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988e3e071fb35d676e641d9410fe4fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d49c9bfb157f8b301579f95558d4c3.png)
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3 . 已知函数
(
是非零实常数)满足
,且关于
的方程
的解集中恰有一个元素.
(1)求
的值;
(2)在直角坐标系中,求定点
到函数
图像上任意一点
的距离
的最小值;
(3)当
时,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2fc102eefee36185e3863b742df6290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e817f37f5a814e856ebc4a16d676ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)在直角坐标系中,求定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4323dcce28ed1206e6ff65600d0dc9e7.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c44faf82ccaf595aa43ad7e4d41e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eefd20b5e8147ce41d2369fbb1334d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-01-16更新
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407次组卷
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3卷引用:上海市南洋模范中学2017-2018学年高一上学期期中数学试题
上海市南洋模范中学2017-2018学年高一上学期期中数学试题江苏省南通市如东高级中学2020-2021学年高二上学期10月月考数学试题(已下线)专题10 《直线与方程》中的取值范围与最值问题(2)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
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4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27579696871a3abf8d0f90d4241640e5.png)
(1)若
,
,求不等式
的解;
(2)对任意
,
,试确定函数
的最小值
(用含
,
的代数式表示),若正数
、
满足
,则
、
分别取何值时,
有最小值,并求出此最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27579696871a3abf8d0f90d4241640e5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ec4add31dd4c2d48aadbb7bd13e607.png)
(2)对任意
![](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/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d665ed88614a7fb9c8d59fb6791c08.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/ac047e91852b91af639feec23a9598b2.png)
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2019-11-15更新
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294次组卷
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2卷引用:上海市上海交通大学附属中学2019-2020学年高一上学期期中数学试题
名校
解题方法
5 . 已知函数
的表达式为
,且
(
).
(1)求实数
的值;
(2)判断函数
的奇偶性并证明;
(3)判断函数
的单调性,并解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed076f12a4e431bc71f43556c0c747d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d1fe42ce285c0c2a0d1880a8dca6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24736c6e9487e5af65d29dd85fa9949a.png)
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2023-12-15更新
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270次组卷
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5卷引用:上海市南洋模范中学2022-2023学年高一上学期11月月考数学试题
上海市南洋模范中学2022-2023学年高一上学期11月月考数学试题(已下线)5.2函数的基本性质(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高一数学精品教学课件(沪教版2020必修第一册)上海市卢湾高级中学2023-2024学年高一上学期期中数学试题(已下线)5.2.1 函数的奇偶性-数学同步精品课堂(沪教版2020必修第一册)广东省深圳科学高中2022-2023学年高一上学期期中数学试题
名校
解题方法
6 . 已知函数
的定义域为
,其图像是一段连续曲线,
在
上是严格减函数,对任意的
、
,恒有
,且
,
.
(1)判断函数
的奇偶性,并证明;
(2)证明:方程
在区间
上有解;
(3)当
时,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5432187d1c042787433b7633292d00fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf3d92544c8a289600641b527b90aaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8718f486c48b09ffd904ddbf1dc7037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a217c3e7cc4d04a0131eac3558673afb.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)证明:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49df07d39e0f9a816eeb02514edb7e06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8845cb12fed2bfc31c235393c619fb15.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84131e431e5a54f51f74e53f486394b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819fb99a322adf0d38857e3e5a360d27.png)
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2023高一·全国·专题练习
7 . 用区间表示下列集合 :
(1)
;
(2)不等式
的所有解组成的集合.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8881e23e6723219021531c48c42e6119.png)
(2)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e8ca0ea50903d2fe881dc9caca9671.png)
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8 . 已知关于x的不等式
有实数解,则实数a的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a5d930c8f40b2cc4c2b63eb45f32f7.png)
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2023高一·上海·专题练习
9 . 用区间表示下列集合 :
(1)
;
(2)不等式
的所有解组成的集合.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd60fb66a3de94c462a914a4dcc6e315.png)
(2)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e8ca0ea50903d2fe881dc9caca9671.png)
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10 . 若关于
的不等式
有唯一实数解,则实数
的值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eaf49ccb8c2d8f7b14c644c1aa0d124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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