名校
解题方法
1 . 定义在
上的函数
满足
,且对任意的
(其中
)均有
.
(1)判断并证明函数
的奇偶性;
(2)若
对所有
恒成立,求实数
的取值范围;
(3)若(1)中的函数
的图象是经过
和
的一条直线,函数
的定义域为
,若存在区间
,使得当
的定义域为
时,
的值域也为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7a77d30c7e410321b05c87af92afe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e32125207addc3fdb92ceb0ec80ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef1e839c3ddd3047b448ae6f8fe7e6f.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0f96b88c346f396d9bbc65ad44d738.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9883c87fe52e83a94f6edf790bd1ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c395021157c73ac8dcde32864f7e121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若(1)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b093b467e4d9a3b8186d2e11f72fdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0195f699765021e2c6ea985e487971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-01-10更新
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2卷引用:安徽省六安市第二中学2023-2024学年高一上学期期末数学试题(一)
名校
2 . 已知
是定义在
上的奇函数,且当
时
.
(1)求函数
的解析式,并画出函数图象;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5397ee1eb6d157f6ec1e7a878f8d16e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bab836364aa5a52e19314e8b9364dec.png)
您最近一年使用:0次
名校
3 . 已知定义在
上的函数
对任意实数
、
,恒有
,且当
时,
,
.
(1)求
的值;
(2)求证:
为奇函数;
(3)求
在
上的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49074b2fc18e7edb1b3b6b4e6f9737c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127d6695d33a50bad7d672680b851f99.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8272c51d4228eaae3deede2017d1e27.png)
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10卷引用:安徽省2023-2024学年高一上学期期末模拟考试数学试题
安徽省2023-2024学年高一上学期期末模拟考试数学试题内蒙古自治区科尔沁2023-2024学年高一上学期期末综合测试数学试题( 一)内蒙古通辽市科尔沁2023-2024学年高一上学期期末综合测试数学试题(二)(已下线)高一上学期期末数学模拟试卷(人教A版2019必修第一册全部)-【题型分类归纳】(人教A版2019必修第一册)(已下线)高一上学期期末数学试卷(巩固篇)-举一反三系列河北省唐山市2023-2024学年高一上学期期末模拟数学试题(已下线)第05讲:函数基础知识和基本性质-《考点·题型·难点》期末高效复习(已下线)专题04 函数的性质与应用2-期末复习重难培优与单元检测(人教A版2019)北京市第十一中学2019-2020学年高一上学期期中数学试题甘肃省白银市第十中学2021-2022学年高一上学期期中考试数学试题
4 . 已知函数
(
,且
)的图象关于坐标原点对称
(1)求实数
的值
(2)比较
与
的大小,并请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9123140bf28567945cc3c6f2d3a40b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347bb4ffedcbea2f4c16d047a138d75.png)
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2024·全国·模拟预测
名校
5 . 已知定义域为
的增函数
满足对任意的
都有
,函数
满足
,且
时,
.若
在
上取得最大值时
的值从小到大依次为
,取得最小值时
的值从小到大依次为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3475cf204ad260614b687c49ee0bd862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f455f43179bcf5c4ffa1575deed5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132d41feaf28a5d96470d23780262b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388141c33eea9e11831be8c061283570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec0ef4d624a3e7b2c420af3365009951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fc692827ffb41809f7f5417a5a3726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b07e1300b0ad772d442b927145b04d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6405e0a390ec82cd87fd4b06ab5df898.png)
A.2800 | B.2700 | C.2600 | D.2500 |
您最近一年使用:0次
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|
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4卷引用:安徽省六安市第二中学2023-2024学年高一上学期期末数学试题(一)
安徽省六安市第二中学2023-2024学年高一上学期期末数学试题(一)(已下线)2024年普通高等学校招生全国统一考试数学理科预测卷(二)河南省安阳市第一中学、安阳正一中学等学校2023-2024学年高一上学期1月期末联考数学试题(已下线)专题4 抽象函数问题(过关集训)(压轴题大全)
6 . 已知
是定义域为
的奇函数,且当
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68c08df2c0aadb1c3084ee738e2a7b5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5641a13aa295dfd45bb2cc9f60e2734d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68c08df2c0aadb1c3084ee738e2a7b5.png)
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5卷引用:安徽省滁州市新锐高级中学2023-2024学年高一上学期12月月考检测数学试题
名校
7 . 已知函数
是奇函数
(1)求实数
的值;
(2)当
时,对于
,不等式
恒成立
,求
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28225bec2b4d5c537dfa9f5f0dfb5667.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c780149aef1bd77162e85f7f8906a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78f247a1c5b1361867e0dc2afa41c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5966b47420c4f711333f143c3acb959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
8 . 函
的定义域为
,且满足
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216075151b30ef946675d50ab3001d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2acd5d8b23f27aa2025fa6f037d2ca08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58eb41ad20e38592d47c04bbbd281ebd.png)
A.![]() | B.![]() | C.2 | D.1 |
您最近一年使用:0次
名校
解题方法
9 . 若集合
中恰有
个元素,则称函数
是“
阶准偶函数”.已知函数
是“2阶准偶函数”,则
的取值范围是________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49387f7cd88490ab8c48ea163d4af37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309c33435e66a747cda2967ccea6d6bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
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3卷引用:安徽省安庆市第一中学2023-2024学年高一上学期12月“三新”检测考试数学试题
安徽省安庆市第一中学2023-2024学年高一上学期12月“三新”检测考试数学试题(已下线)考点3 与集合相关的新定义问题 --2024届高考数学考点总动员【练】云南省昭通市教研联盟2023-2024学年高一上学期期末考试数学试卷
名校
10 . 对于任意两个正数
,记曲线
直线
轴围成的曲边梯形的面积为
,并约定
和
,德国数学家莱布尼茨
最早发现
.关于
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928039b9b646389e86fb2626a9796984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5191d24feca9123d69a91384c9c4e670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1985cc620ee5113757a8ff82ab81e36c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f876a9bf2d12e1f396448e62e06dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d892d558ef10601ac517db8b86c3fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95dada351eed776f45bbad99fd57028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7bf24fa36d4a3ddc44f212cae688c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1985cc620ee5113757a8ff82ab81e36c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4卷引用:安徽省安庆市第一中学2023-2024学年高一上学期12月“三新”检测考试数学试题