1 . 已知函数
,
.
(1)若
是奇函数,求a的值并判断
的单调性(单调性不需证明);
(2)对任意
,总存在唯一的
,使得
成立,求正实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c064cd16c1c95023009c344564a1022a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad0bcb38bd67c085ab01b13cf7a3e05.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3715365d7cf7959b963815c32327c4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30a4750430b4b0e9daa3edbef242184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
您最近一年使用:0次
2023-06-12更新
|
1352次组卷
|
3卷引用:2023年6月浙江省学业水平适应性考试数学试题
名校
2 . 已知函数
,
.
(1)记
在
上的最大值为
,最小值为
.
(i)若
,求
的取值范围;
(ii)证明:
;
(2)若
在
上恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97bb437f1b1904f3487c1df9caeac35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ea91b3b73ac79e87ce48a2afd49652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c258e64c4baa12143732662859a535c2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb7bae6e61454acbadc2a13b7c39783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-11-30更新
|
437次组卷
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2卷引用:浙江省台州市五校联盟2020-2021学年高一上学期期中数学试题
19-20高一·浙江·期末
3 . 设
,若函数
定义域内的任意一个x都满足
,则函数
的图象关于点
对称;反之,若函数
的图象关于点
对称,则函数
定义域内的任意一个x都满足
.已知函数
.
(Ⅰ)证明:函数
的图象关于点
对称;
(Ⅱ)已知函数
,若对任意的
,总存在
,使得
成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5ca6a673a07fe420e017b3e24d3887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5ca6a673a07fe420e017b3e24d3887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9948707cc99ebd8c167a463aafd62f.png)
(Ⅰ)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0973c965c9ae00beec9f04e8d2aecb02.png)
(Ⅱ)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3cca387f5f72ffe9bbcfe4a801f3ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5d499666f20047af33ad30482efd37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff2ed174d15f39702542c273eb563b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0cc1a35f4aa0cfc29e5b7215bcff19d.png)
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解题方法
4 . 已知函数
,
(1)当
时,若
且
,证明:
;
(2)当
时,若
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdf69b4d0d110205b2024430b670446c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b70f8691af2a1d287aa5c476ede5e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbf8da534490147db4fee75f71a4c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f774df9caef9535f3506730284183738.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6343069217cd6d8dd32446da428dae46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d026de72fab7e92f39f461e41be3a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219ba6c8a1b54598db1a78cab28d9d30.png)
您最近一年使用:0次
名校
5 . 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
|
842次组卷
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4卷引用:浙江省2016年4月普通高中学业水平考试数学试题
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【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(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)