名校
1 . 已知函数
(
为实常数且
).
(Ⅰ)当
时;
①设
,判断函数
的奇偶性,并说明理由;
②求证:函数
在
上是增函数;
(Ⅱ)设集合
,若
,求
的取值范围(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99fcef3856a1d67acab12b85b5a4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da67075d5f20954afe0232112e159ac9.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd88b374924344fb157a15c2d36edad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
②求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9006ed5e53e4637fbacec7832dfe2146.png)
(Ⅱ)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d56bb1ee8639cb81434e10cb3c9a0cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4815b1d16a7ae485ff0bba0b397e893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
您最近一年使用:0次
2018-11-01更新
|
845次组卷
|
4卷引用:【全国百强校】江西省新余市第四中学2018-2019学年高一10月月考数学试题
【全国百强校】江西省新余市第四中学2018-2019学年高一10月月考数学试题浙江省2016年4月普通高中学业水平考试数学试题浙江省金华市第一中学2021-2022学年高一上学期期中数学试题(已下线)专练29 期中综合检测AB卷-2021-2022学年高一数学上册同步课后专练(人版A版2019必修第一册)
解题方法
2 . 已知函数
是偶函数.
(1)求证:
是偶函数;
(2)求证:
在
上是增函数;
(3)设
(
,且
),若对任意的
,在区间
上总存在两个不同的数
,使得
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e1c34e767abf34e4e1c1a4e41877ca.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139af8e9594559f2f33dbdce3372ad9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e17fdff31f9f9fab12e62dd62c189e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c33b69adc112831fa115b5dffdb616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61517b49be9272b31b8d8651fc2f79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
3 . 设
,
,在集合
的所有元素个数为2的子集中,把每个子集的较大元素相加,和记为
,较小元素之和记为
.
(1)当
时,求
,
的值;
(2)求证:为任意的
,
,
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1534b035eca39010118a83486de8904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/330a768883271ebe0b692f6c226867a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6862dd3c43647ce7d7935a7d205b54d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求证:为任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1534b035eca39010118a83486de8904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f563f31a226905e5b38ca81078a1af35.png)
您最近一年使用:0次
2018-06-23更新
|
1103次组卷
|
2卷引用:【全国百强校】江苏省泰州中学2017-2018学年高二6月月考数学(理)试题
名校
4 . 已知集合
,其中
,
,
.
表示
中所有不同值的个数.
(
)设集合
,
,分别求
和
.
(
)若集合
,求证:
.
(
)
是否存在最小值?若存在,求出这个最小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9e56ab45ddf991ae24983027e04b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0c23fa72e4bbbdef69895aef768c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153fb853cd99beec9e600a4eaf73fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403eef43448ff6ba342ed0ad5c4b5978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28542a0186cd714deaa181efadff87cd.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef27cd09f4ecc055fd7e72b3b368e5df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746a3b7cb3c7ac223c8aa0d4b93ae093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3851739b3d70143beaca9621b265871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce6942492388c0805d27db3a9b8a345.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972fd1bc03c253c043535a8425cfabab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5675fc66a66c7cd74516987fa758984.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403eef43448ff6ba342ed0ad5c4b5978.png)
您最近一年使用:0次
2018-03-30更新
|
574次组卷
|
4卷引用:北京市东城东直门中学2017-2018学年高三上期中数学试题
北京市东城东直门中学2017-2018学年高三上期中数学试题北京市海淀区教师进修附属实验学校2019~2020学年高一第二学期期中考试数学试题(已下线)数学-6月大数据精选模拟卷05(北京卷)(满分冲刺篇)北京市宣武外国语实验学校2021届高三上学期期中考试数学试题
名校
5 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3717ef8837dc2941ed6a187bb1ff1148.png)
(1)判断函数
的奇偶性,并说明理由.
(2)判断函数
在
单调性,并证明你的判断.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3717ef8837dc2941ed6a187bb1ff1148.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
您最近一年使用:0次
2017-11-28更新
|
521次组卷
|
3卷引用:山西省太原市2017-2018学年高一上学期第一次测评(期中)数学试题
10-11高二下·广东梅州·期末
名校
6 . 设函数
的定义域是R,对于任意实数
,恒有
,且当
时,
.
(1)求证:
,且当
时,有
;
(2)判断
在R上的单调性;
(3)设集合A=
,B=
,若A∩B=
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac82501b461d044f78e7ae5b86cd3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be4ab7d32ed15c176c550d8543ab369.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设集合A=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090837c3bd5bb38c27c4771f941cde79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a4b9c344e783bd8044155dbde7b6c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2017-11-12更新
|
1049次组卷
|
6卷引用:2010-2011学年梅州市曾宪梓中学高二第二学期期末考试数学(文)
(已下线)2010-2011学年梅州市曾宪梓中学高二第二学期期末考试数学(文)(已下线)2012届河南省卢氏一高高三适应性考试理科数学2015-2016学年山西省康杰中学高二下期末文科数学试卷广西南宁市第三中学2017-2018学年高一上学期期中考试数学试题【校级联考】江西省上饶市“山江湖”协作体2018-2019学年高一(上)第三次月考数学试题河南省实验中学2019-2020学年高一上学期10月月考数学试题
名校
7 . 设
为实数,函数
.
(1)求证:
不是
上的奇函数;
(2)若
是
上的单调函数,求实数
的值;
(3)若函数
在区间
上恰有3个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30488993ac8cb5775026ffd59e63b927.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)若
![](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/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2017-08-13更新
|
1330次组卷
|
2卷引用:江苏省南通市海安高级中学2016-2017学年高一下学期期末考试数学试题
8 . 已知函数
.
(1)判断函数
的奇偶性;
(2)对任意两个实数
,求证:当
时,
;
(3)对任何实数
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956f5a1abb489955154b94cd109ecc0b.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对任意两个实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec808ad60dbf016632ec816eaca1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d47c1b2254840eb6c54ec0c6214990.png)
(3)对任何实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c89395a55f310aadbb0d9698af5e42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
9 . 定义在
上的函数
,如果对任意的
,都有
成立,则称
为
阶伸缩函数.
(
)若函数
为二阶伸缩函数,且当
时,
,求
的值.
(
)若
为三阶伸缩函数,且当
时,
,求证:函数
在
上无零点.
(
)若函数
为
阶伸缩函数,且当
时,
的取值范围是
,求
在
上的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c170c6edcf12a405c10a953df1eba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46ecf935049473045cdebae68415657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb73fa3b190cf93a602f12466901c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443fbb92a82fb4c57b34f505ed60735d.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6c4782b2114209b906b06f284ab720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7444d84d848c1d0e5f017694f88b53d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39f59f3af3784e7e87bef70122c7d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc07b986f375453663b3e5c93eb1e0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ae66c5401deed7341470ca37800463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c769af02c1e75287e56632714c57017c.png)
您最近一年使用:0次
2017-07-21更新
|
442次组卷
|
2卷引用:湖南省衡阳市第八中学2016-2017学年高一下学期理科实验班结业(期末)数学试题
解题方法
10 . 在平面直角坐标系
中,将从点
出发沿纵、横方向到达点
的任一路径称为
到
的一条“折线路径”,所有“折线路径”中长度最小的称为
到
的“折线距离”.如图所示的路径
与路径
都是
到
的“折线路径”.某地有三个居民区分别位于平面
内三点
,
,
,现计划在这个平面上某一点
处修建一个超市.
![](https://img.xkw.com/dksih/QBM/2017/5/10/1683970740789248/1715263246712832/STEM/5a37f9ceff464a899e865c12f92b60c1.png?resizew=237)
(1)请写出点
到居民区
的“折线距离”
的表达式(用
表示,不要求证明);
(2)为了方便居民,请确定点
的位置,使其到三个居民区的“折线距离”之和最小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb9227785322ac87fe538f3164f30dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d3a701135e9a11b344e2f8bff95410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627f1578beab2071cefd6cb0278b57f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79485e42b7546ccfa3cd6d08491460f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7685ae8254f0b1442482c892d039ae0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://img.xkw.com/dksih/QBM/2017/5/10/1683970740789248/1715263246712832/STEM/5a37f9ceff464a899e865c12f92b60c1.png?resizew=237)
(1)请写出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
(2)为了方便居民,请确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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