名校
1 . 已知函数
是
上的增函数,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97c556daceff1b59b724104b0d859a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
2 . 已知
,
.
(1)若
,判断
的奇偶性.
(2)若
是单调递增函数,求
的取值范围.
(3)若
在
上的最小值是3,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87ecbabf349ed188fb1dcee2a4c8a24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec90f93919eb1d1a6b0ed9d05bf91c02.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9099a75c433e97bbe05052a00110571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
3 . 已知函数
,其中常数
.
(1)若函数
分别在区间
,
上单调,求
的取值范围;
(2)当
时,是否存在实数
和
,使得函数
在区间
上单调,且此时
的取值范围是
.若存在,求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea96d9c85876681749d9091d2f82fa8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189b2da6c420bf8f8900002d14f65f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8af7bed124f00c8e19b52d028b4d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-01-29更新
|
175次组卷
|
2卷引用:浙江省杭州第二中学2023-2024学年高一上学期期中考试数学试题
4 . 已知函数
,
,
(1)解关于x的不等式
;
(2)从①
,②
]这两个条件中任选一个,补充在下面问题的横线处,并给出问题的解答.
问题:是否存在正数t,使得 ?若存在,求出t的值:若不存在,请说明理由.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e5e15e7cc7fc9aee815f987eaf39fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
(1)解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fed773e88a9fb0bb42b8bc8f0f0a34f.png)
(2)从①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5113b136023b32e0813fb3a823537d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623c0f25f853eebff06fa188dc8f820.png)
问题:是否存在正数t,使得 ?若存在,求出t的值:若不存在,请说明理由.
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e5c9aeb6712775b572c64f3512887d.png)
(1)当
时,求函数在区间
上的值域;
(2)函数
在
上具有单调性,求实数
的取值范围;
(3)求函数
在
上的最小值
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e5c9aeb6712775b572c64f3512887d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9c64ba837387d640de4b8e2191b1b5.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726c255e5f5ed80378bcbe5b9913a6ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5432187d1c042787433b7633292d00fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a7b7c834d06f3e28a339db94690172.png)
您最近一年使用:0次
2023-11-28更新
|
275次组卷
|
2卷引用:四川省泸州市古蔺县蔺阳中学校2023-2024学年高一上学期期中考试数学试题
名校
解题方法
6 . 设函数
(
为常数)在
上严格递减,在
和
上严格递增,且
的部分图像如图所示,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8255d540afdd24f608ab7ec231cff469.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa8e9f8800cffadd4d4a77caa01f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68aeaab00b18ca6dbddfa93167c4d73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8255d540afdd24f608ab7ec231cff469.png)
您最近一年使用:0次
2023-11-25更新
|
367次组卷
|
3卷引用:上海市格致中学2023-2024学年高三上学期期中考试数学试卷
名校
解题方法
7 . 已知函数
的图象可由函数
(
且
)的图象先向下平移2个单位长度,再向左平移1个单位长度得到,且
.
(1)求
的值;
(2)若函数
,证明:
;
(3)若函数
与
在区间
上都是单调的,且单调性相同,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e6f7234a6a37987de4cdce6f026331.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/93acdd1905e7b9374f0644820fb3fd71.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f4b6dabbadf37d201eadf7486dc98c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abea70e7e8122478683bc072aa38095.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b9a99afeadaec62a56019ff61e04c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496fd07ac35a34a6d0edfead2aeef41a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-11-23更新
|
345次组卷
|
2卷引用:河南省部分学校2023-2024学年高一上学期期中大联考数学试题
名校
8 . 一般地,若函数
的定义域为
,值域为
,则称
为
的“
倍跟随区间”;特别地,若函数
的定义域为
,值域也为
,则称
为
的“跟随区间”.下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62e0a7ec931569bcc9c911f2c249d56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.函数![]() |
B.若![]() ![]() ![]() |
C.二次函数![]() |
D.若函数![]() ![]() |
您最近一年使用:0次
2023-11-22更新
|
313次组卷
|
3卷引用:安徽省六安第一中学2023-2024学年高一上学期期中考试数学试题
名校
解题方法
9 . 已知指数函数
(
且
)在其定义域内单调递增.设函数
,当
时,函数
恒成立,则x的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d894b0a2edbe018fd3578a37b1ead047.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/32b447cf39cab4a304a236ac23d88713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700aa260b897caf06b0a8341f2178a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85187c85826beeca12137805293fff77.png)
您最近一年使用:0次
2023-11-19更新
|
599次组卷
|
4卷引用:广东省深圳市福田区深圳市高级中学2023-2024学年高一上学期期中数学试题
广东省深圳市福田区深圳市高级中学2023-2024学年高一上学期期中数学试题(已下线)4.2.1指数函数的概念+4.2.2指数函数的图象和性质【第三课】河南省鹤壁市高中2023-2024学年高一上学期第三次段考数学试题河南省南阳市社旗县第一高级中学2024届高三上学期1月月考数学试题
名校
10 . 已知函数
的定义域为
,若
在
上为增函数,则称
为“一阶比增函数”.
(1)若
是“一阶比增函数”,求实数
的取值范围;
(2)若
是“一阶比增函数”,求证:
,
,
;
(3)若
是“一阶比增函数”,且
有零点,求证:
有解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e82cc461b9607e08a8b31597f6d26df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbd41b395876a630b360b2a34acbcd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1a5699410baa270f3fa8153ab346e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe66bbf8d1c5647038819e31d88015.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b244b324e93c98de88fbffa52fc103f1.png)
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