1 . 已知函数
在区间[2,3]上有最大值4,最小值1.函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84f1b450c7b6a33036a323d97a1e354.png)
(1)求函数g(x)的解析式;
(2)若存在
使得不等式f(lnx)-klnx≤0成立,求实数k的取值范围;
(3)若函数
有三个零点,求实数k的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de8b0a5c3007bfe73dfa36be264f074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84f1b450c7b6a33036a323d97a1e354.png)
(1)求函数g(x)的解析式;
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6957c74475ce7b08482971e37c242a.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd919fbd59680a392c78af922b68014.png)
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2 . 已知函数
.
(1)根据a的不同取值,判断函数
的奇偶性(只写结论,不需证明);
(2)设函数
,当
时,对于
,总有
成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ac7df0685ba0947428ad4b7f99622a.png)
(1)根据a的不同取值,判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22382e94f33493220314c2a5ace3b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ccb51adec8cde167e2198ada879e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb184f810b48f7dcda528c76acf33ab.png)
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名校
解题方法
3 . 定义两类新函数:
①若函数
对定义域内的每一个值
,在其定义域内都存在唯一的
,使得
成立,则称该函数为“
函数”;
②若函数
对定义域内的每一个值
,在其定义域内都存在唯一的
,使得
成立,则称该函数为“
函数”.
(1)设函数
的定义域为
,已知
是某一类新函数,试判断
是“
函数”还是“
函数”(不需说明理由),并求此时
的范围;
(2)已知函数
在定义域
上为“
函数”,若存在实数
,使得对任意的
,不等式
都成立,求实数
的取值范围.
①若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.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/c411a8fd18c8de5c7de91ead2534602b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a83c952b58c39be1b0d43d304e0911.png)
②若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.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/c3c98c995fc2687a803998d262d754e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdf896f6685774c416482a887484fc0.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da9ea25accbf7eeb60424224b68c092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a83c952b58c39be1b0d43d304e0911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdf896f6685774c416482a887484fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c918ca5d4e6d46ed130f85e5fa608d.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53275eb34d75ead1b48d1d78123d536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56002ab09438fcb642fde70b10ee9720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdf896f6685774c416482a887484fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06f45220c23094a3d9ef53b54b89d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94526b73a995b128c50c2487e192f057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2020-08-07更新
|
594次组卷
|
2卷引用:安徽省合肥市第六中学2019-2020学年高一下学期学情检测数学试题
4 . 已知
,
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d671628856390127cbffd2f8bd098e.png)
(1)当
时,请写出
的单调递减区间;
(2)当
时,设
对应的自变量取值区间的长度为l(闭区间
的长度定义为
)求l关于a的表达式,并求出l的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43be8655375defb2d244844cbba59ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55b6ea77ab1bb966da0ca0e73b97dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d671628856390127cbffd2f8bd098e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a59011b33c66ca24e0fed4243b8e704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e669d502287cab6a74d72fb4aa1ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
您最近一年使用:0次
5 . 已知二次函数
满足下列3个条件:
①
的图象过坐标原点;②对于任意
都有
;③对于任意
都有
.
(1)求函数
的解析式;
(2)令
.(其中m为参数)
①求函数
的单调区间;
②设
,函数
在区间
上既有最大值又有最小值,请写出实数p,q的取值范围.(用m表示出p,q范围即可,不需要过程)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00cbf67f0605a8d1f4499b156785001f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b129a86f37fbbdf5a5808f13924e819f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b45f20b8f07836bb5d9941ae862233.png)
①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e257b2b02bcd57c116841807979bbc.png)
您最近一年使用:0次
2020-01-04更新
|
393次组卷
|
3卷引用:【市级联考】江苏省扬州市2018—2019学年高一第一学期期末检测试题数学
名校
6 . 已知函数
在区间
上是单调函数.
(1)求实数
的所有取值组成的集合
;
(2)试写出
在区间
上的最大值
;
(3)设
,令
,若对任意
,总有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dfe62bb9beac0720d3c6fa3155207a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)试写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1987ecbd076d89da5ef1e2561d79d857.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8fcf119beecdeda292c6db685ca16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e540d5da966481bd552eb01187bc12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930995172d12e12d8173aec823f1982b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd5eb1e81ec6f44e4cb59ce214b949a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-11-19更新
|
581次组卷
|
2卷引用:浙江省浙东北联盟(ZDB)2019-2020学年高一上学期期中数学试题
名校
7 . 设函数
(其中
为常数).
(1)根据实数
的不同取值,讨论函数
奇偶性;
(2)若
,且
在区间
上单调递减,求实数
的取值范围;
(3)若关于
的不等式
在
时恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef79a4c2851a7e5e24018fd076406da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)根据实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55fc27d9554bc93298f29373f4e9e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13e38a5ee18ecf4af2d9a8443b4a7bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a749285bc6d24bc6e3c27157ef20a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
8 . 函数
.
(1)根据
不同取值,讨论函数
的奇偶性;
(2)若
,对于任意的
,不等式
恒成立,求实数
的取值范围;
(3)若已知
,
. 设函数
,
,存在
、
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db58afeac1cfe83233a8887e16f59b7.png)
(1)根据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa43aa41923960f8af7e8f1b1bd1695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7aede2e847d081811f62ce462906167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64587952d138b00a1c463df835f5500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032e8dc00cdc96860c9cbf8ac09677fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2019-12-09更新
|
659次组卷
|
3卷引用:上海市新川中学2018-2019学年高三上学期10月月考数学试题
名校
解题方法
9 . 设函数
,
(1)若不等式
在
内恒成立,求
的取值范围;
(2)判断是否存在大于1的实数
,使得对任意
,都有
满足等式:
,且满足该等式的常数
的取值唯一?若存在,求出所有符合条件的
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7731cafe2b96055e1d95c28579a3d4fe.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f526c68384da7f5ad0d04ac2eebd07ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d26f643f896eda71a2485bd8e41de95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断是否存在大于1的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831fcf5f7fa0042343e389a9d5f9441c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abde3c424688925673deb962002df485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7acd58b7a7be29bdd0352a0a266cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2016-12-03更新
|
599次组卷
|
4卷引用:2014-2015学年重庆市万州中学高一上学期12月月考数学试卷
2014-2015学年重庆市万州中学高一上学期12月月考数学试卷【校级联考】四川外语学院重庆第二外国语学校2018-2019学年高一上学期第二次月考数学试题(已下线)第17讲 双元恒成立与有解问题-【提高班精讲课】2021-2022学年高一数学重点专题18讲(沪教版2020必修第一册,上海专用)(已下线)第五章 函数的概念、性质及应用(6大易错与5大拓展)(2)-单元速记·巧练(沪教版2020必修第一册)
10 . 对于在区间
上有意义的两个函数
与
,如果对任意的
,均有
,则称
与
在
上是接近的,否则称
与
在
上是非接近的.现在有两个函数
与
,现给定区间
.
(1)若
,判断
与
是否在给定区间上接近;
(2)若
与
在给定区间
上都有意义,求
的取值的集合
;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
(3)在(2)的条件下,是否存在
,使得
与
在给定区间
上是接近的;若存在,求
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5aff60e0e18dec5ddfa15bd1d91958e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0597404b9110a0e25b644c9e51aabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d220d623c5e1f0be00b173ba524dfba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a9ca12b588bb208de5e7da200c7272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d9b91bab8bc82f119216cc743c8dbb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3129ddd2ea97fd010b9e0b644225da8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d9b91bab8bc82f119216cc743c8dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
(3)在(2)的条件下,是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f1ecfcbe90dca8dc8f3aa7ebaccfb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d9b91bab8bc82f119216cc743c8dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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