解题方法
1 . 已知函数
是定义在
上的偶函数,当
时,
.
(1)当
时,求函数
的解析式;
(2)用定义证明函数
在区间
上是单调增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a28068770a85b88b42321cd71ecd3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5dbfac684b9901a16ae61dbaa0f817.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)用定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
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2022-03-30更新
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3卷引用:江苏省常州市八校2021-2022学年高一上学期12月联考数学试题
江苏省常州市八校2021-2022学年高一上学期12月联考数学试题(已下线)期末测试卷02(基础卷)-【满分计划】2022-2023学年高一数学阶段性复习测试卷(苏教版2019必修第一册)天津市实验中学滨海学校2023-2024学年高一上学期期中数学试题
名校
解题方法
2 . 已知函数
是定义在
上的奇函数,
(1)求
的值;
(2)设函数
,判断
的单调性,并用定义证明你的结论;
(3)若函数
(其中
)在
的最小值为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d335174c6030a3dcefd619db5ba0e762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49763a13356caea193bd86baf16ed54d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8d152b604f4ac623621db4fde59b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee68b6458860e5b03a6dfae8a535aa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2022-07-01更新
|
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3卷引用:江苏省南京市大厂高级中学2021-2022学年高二下学期6月阶段调研测试数学试题
名校
3 . 设二次函数
.
(1)若
,
且二次函数的最大值为正数,求
的取值范围.
(2)若
的解集是
,求
的解集.
(3)设二次函数
的两个零点分别为
,
,满足
,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8352b2e643a7ce605334f1b0e572bfb0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ea0e903fbb4c8ce04133b9969578c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566bfdd14f1aa396f620e0ca6895a21c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f3d2d9f66307b7af2398efdb893bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa220ab7c91ffa40202bcc544aa2bb2.png)
(3)设二次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd69aebdafb31468eb13ce3b28a36e47.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/57cfda1c04b6eaeb5e78018539c2880e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e37902f139fee3d5a5ac74b21b0a0e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1ad9f639b70bf98fe33ca163a8922f.png)
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4 . 已知集合M是非空数集,且满足三个条件:①∀x∈M,∀y∈M,恒有x﹣y∈M;②∀x∈M(x≠0),恒有
;③1∈M.
(1)判断
是否正确,说明理由;
(2)求证:∀x∈M,∀y∈M,恒有x+y∈M.
(3)求证:当x≠0且x≠﹣1时,x∈M”是“
∈M”的充分条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ac8248bb70f9ef5b0cb7d025e05160.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de68508dc0a95fc4b5de772390260db.png)
(2)求证:∀x∈M,∀y∈M,恒有x+y∈M.
(3)求证:当x≠0且x≠﹣1时,x∈M”是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66608ce1eb4cb750b25174e150981c72.png)
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解题方法
5 . 已知函数
.
(1)若
,且
在区间
恒成立,求
的取值范围;
(2)当
,
时,求证:在区间
至少存在一个
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80a126420532d7b9abd59d163436fb4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71eda28755639d00f9d24b95679d9496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3417699eb4a32521b7ff1f7b2a1d5f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ed0edaebe95e5347b44806e166d0e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a03974ef6cb941dea8f00a172e8b99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c275d203295b989c129101d82e74ae01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1055a901cc9598d4bf9fb42144ce6d.png)
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6 . 已知函数
,
.
(1)求证:
为R上的偶函数;
(2)若函数
在R上只有一个零点,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4b13834f3ca8e3ec9e20bd6c02bd35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964a86e1c993a63710fd1c329e2dd37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-01-20更新
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557次组卷
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2卷引用:江苏省常州市教育学会2021-2022学年高一上学期学业水平监测数学试题
7 . 设a是实数,函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0a9ba8c8e14d2cda6941002aefe6de.png)
(1)求证:函数
不是奇函数;
(2)若
在
单调递减,求满足不等式
的x的取值范围;
(3)求函数
的值域(用a表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0a9ba8c8e14d2cda6941002aefe6de.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd3f86cd7afe812f3d8e131bee1e315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fce155963060b2e5b9147a185897cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb58ed6cf8c804fe62a59dcf3c73f4c1.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
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8 . 已知函数
(
且
).
(1)判断并证明函数
的奇偶性;
(2)若
,求函数
的值域;
(3)是否存在实数a,b,使得函数
在区间
上的值域为
,若存在,求a,b的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7454b159d49d842623b993b97f7fd779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d69c8147dd7b7c1a46739e30c595fa.png)
(3)是否存在实数a,b,使得函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff3a5e9128e2f2102d0dc645a87811f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
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2022-01-22更新
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7卷引用:江苏省南通市海安市实验中学2022-2023学年高一下学期第一次学情检测数学试题
名校
9 . 已知a,b均为正实数,且
.
(1)求
的最大值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b40b1544e62be8b9e9f4dc9f2c0c74.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438dff4764605c96d152afd661f89804.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c73593af98298c581995ba919ae3667.png)
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解题方法
10 . (1)已知a,b,x,
,且
,
,试比较
与
的大小.
(2)已知
,
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2519954ec2deabecd7e057886fa4023c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec8201ff29a2091d40eee10db6bbc1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b21208364124b5c477b2ff8df1c2e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ee8a678f431a14c7c6c1a6088d057c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46950cf924aff835a6aa4bf477c27b24.png)
(2)已知
![](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/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f666eada92511beab60540a7e201b769.png)
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2021-11-12更新
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3卷引用:江苏省常州市田家炳高级中学2021-2022学年高一10月份调研数学试题