解题方法
1 . 已知函数
.
(1)用单调性定义证明:
在
上单调递增;
(2)若函数
有3个零点
,满足
,且
.
①求证:
;
②求
的值(
表示不超过
的最大整数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247d7790d83be16bc74aa5e5d12dd63.png)
(1)用单调性定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f8994d83bf4a688c0ab897a5a40fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1cc5cfec94bc5686b41b043acdc8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d995c5d2e1e0305d805032e18997986a.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28cbe8f17c4472d8663f9ccbe3b98f6.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59077d1948911b13d68a572eadbca3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
解题方法
2 . 设函数
的定义域为
.若存在常数
,
,使得对于任意
,
成立,则称函数
具有性质
.
(1)判断函数
和
具有性质
?(结论不要求证明)
(2)若函数
具有性质
,且其对应的
,
.已知当
时,
,求函数
在区间
上的最大值;
(3)若函数
具有性质
,且直线
为其图像的一条对称轴,证明:
为周期函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809ea2eff71a0de3db640313ad25b7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404d068b60dd901194f1684d023212ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8073fa685bc10cf01a0128220feac940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e661ad31aa4c6d8684923cf904bf1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d0588454ec8b64bf86578fb90b39e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55351494cd96fed31976fdc5d9c7292.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
2021-08-01更新
|
588次组卷
|
3卷引用:北京市西城区2020-2021学年高一下学期期末数学试题
3 . 对于函数
及实数m,若存在
,使得
,则称函数
与
具有“m关联”性质.
(1)若
与
具有“m关联”性质,求m的取值范围;
(2)已知
,
为定义在
上的奇函数,且满足;
①在
上,当且仅当
时,
取得最大值1;
②对任意
,有
.
求证:
与
不具有“4关联”性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf557bc0501acbf300fd4ae5993b7242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4870a0f8fee7a8357094ab4309263752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e1ce7071be0743ded4a087fd908eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96101eb5dce02c0213ad008413f3066.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263b718b5b3cbc27f3e0ef94f4157f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18db64040b2fa9d65075b41ada928fa6.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9c839f85fe048ed0882889e22f5166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d2c5422d4b9f8c11a5ad1b62c6bb87.png)
您最近一年使用:0次
2024-01-24更新
|
1190次组卷
|
4卷引用:广东省华南师范大学附属中学2023-2024学年高一上学期期末数学试题
广东省华南师范大学附属中学2023-2024学年高一上学期期末数学试题黑龙江省哈尔滨市第一二二中学校2024届高三下学期校二模考试数学试题河南省郑州市宇华实验学校2024届高三下学期第三次模拟考试数学试题(已下线)压轴题01集合新定义、函数与导数13题型汇总-2
4 . 我们知道:设函数
的定义域为D,那么“函数
的图象关于原点成中心对称图形”的充要条件是“
,
”.有同学发现可以将其推广为:设函数
的定义域为D,那么“函数
的图象关于点(m,n)成中心对称图形”的充要条件是“
,
”已知
.
(1)利用上述结论,证明:
的图象关于点
成中心对称图形;
(2)判断
的单调性(无需证明),并解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57eb010ff662d57396d079222c0cdad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0381746695cc95095bd5f248b707ea1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8f7c92dca9e48db1da75fbad2a7287.png)
(1)利用上述结论,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49a26cf164e6f90fbd6fadd34bb82fc.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5246be48b0389b4a60952950875d352d.png)
您最近一年使用:0次
解题方法
5 . 已知
的定义域为
,且
,且
.
(1)证明
是偶函数;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f6cd8b41d4d12a06a4e84e8c0f0900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ef022cb5ccd3757adda282dccca52b.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c97cdbb3ad27a555f765ccb2436bf9.png)
您最近一年使用:0次
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解题方法
6 . 我们知道,函数
图像关于坐标原点成中心对称图形的充要条件是函数
为奇函数,有同学发现可以将其推广为:函数
的图像关于点
成中心对称图形的充要条件是函数
为奇函数.已知函数
.
(1)利用上述结论,证明:函数
的图像关于
成中心对称图形;
(2)判断函数
的单调性(无需证明),并解关于x的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82aaa597a5aa6176863eda3fdf83e181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085bfb527b2456d52d4a62ab68526389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fed5bea7a73e39134c2e836ac4e054a.png)
(1)利用上述结论,证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f935fa5d0ae1b208aff21aa468ecf8.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d63bcd446673738bbcd8827b06c83a.png)
您最近一年使用:0次
2023-02-22更新
|
1102次组卷
|
4卷引用:四川省绵阳市2022-2023学年高一上学期期末数学试题
四川省绵阳市2022-2023学年高一上学期期末数学试题四川省成都市2023-2024学年高一上学期期末数学练习卷(二)(已下线)专题10 指数及指数函数压轴题-【常考压轴题】(已下线)四川省成都市第七中学2023-2024学年高一上学期12月月考数学试题
7 . “函数
的图象关于点
对称”的充要条件是“对于函数
定义域内的任意x,都有
.”已知函数
的图象关于点
对称,且当
时,
.
(1)求
的值;
(2)设函数
,
(i)证明函数
的图象关于点
对称;
(ii)若对任意
,总存在
,使得
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f941989cf172319ef2dd07b88fe493d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86022205a7487439dd8d0897cd3bf19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f217e309a5f6aba827d9cd8a86bc56a8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73cf5644015fde37797b32062c816ee0.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6bdbd4a58bf065e0d9048f6c3c24e2.png)
(i)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1be9a704175b9d0007658873704d5b1.png)
(ii)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e0e2b0167e90a701048cd992eb5d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0261f256ffa435eef4e06723ce301c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
的定义域为R,其图像关于点
对称.
(1)求实数a,b的值;
(2)求
的值;
(3)若函数
,判断函数
的单调性(不必写出证明过程),并解关于t的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9f1b1e833527b39ad9ea91aea2d1fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a982c17d1a94a9bd81dc27cad133b74.png)
(1)求实数a,b的值;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88afe5c5be8dc12217ccbef588cc61c.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32f81eed27df1b12ed5a6b0268b9f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf72c0b01a74a3bbbca82f6c913ffd5.png)
您最近一年使用:0次
2022-12-30更新
|
797次组卷
|
3卷引用:辽宁省大连市2022-2023学年高一上学期期末数学试题
解题方法
9 . 我们知道,函数
的图象关于坐标原点成中心对称的充要条件是函数
为奇函数,有同学发现可以将其推广为:函数
的图象关于点
成中心对称的充要条件是函数
为奇函数.
(1)若
.
①求此函数图象的对称中心;
②求
的值;
(2)类比上述推广结论,写出“函数y=f(x)的图象关于y轴成轴对称的充要条件是函数y=f(x)为偶函数”的一个推广结论(写出结论即可,不需证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec550c01b4f075f22ab67f5e55ed5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d0969cb7acbeaa05a101a385348a00.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4d0f4b197e56a2c1bfb0822607441f.png)
①求此函数图象的对称中心;
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18cb440e92146010f540eb2947fa0f4.png)
(2)类比上述推广结论,写出“函数y=f(x)的图象关于y轴成轴对称的充要条件是函数y=f(x)为偶函数”的一个推广结论(写出结论即可,不需证明).
您最近一年使用:0次
名校
解题方法
10 . 设函数
的定义域为
,其中常数
.若存在常数
,使得对任意的
,都有
,则称函数
具有性质
.
(1)当
时,判断函数
和
是否具有性质
?(结论不要求证明)
(2)若
,函数
具有性质
,且当
时,
,求不等式
的解集;
(3)已知函数
具有性质
,
,且
的图像是轴对称图形.若
在
上有最大值
,且存在
使得
,求证:其对应的
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c96c44af898dc6e18a56847c9ca9deb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094f977194228bed828f3507f5898934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600e6adb81760e97ef1e96c007135796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b85f6057a2755b0b0e80615b97606a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91b1f16f888091fd0132a29b94ce5e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1c61a14ef7b70f15a83f42ca662ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998485ffeb46a0412ff1a0f814429257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964616795ec19de5861079667b00d8d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702f140de921e15fb5c3b68daa280a6e.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3471484b64504fc545398f52be830010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af908bca1b10f5de7e2d8979989c806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8944bbcea8400d9d7034f8f9a176eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85405de521f9dd48f2a307eb4fdc8b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1a7dc6618e423fe20f80a2aea02097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be895daebbdce508982977a77df16f9.png)
您最近一年使用:0次
2022-07-09更新
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579次组卷
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2卷引用:北京市西城区2021-2022学年高一下学期期末考试数学试题