解题方法
1 . 当
时,函数
在
上的零点的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65cc52aacc31a21a443c8de0374b24f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f7aaddab82e30701ae603267cc89a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
A.4 | B.3 | C.2 | D.1 |
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解题方法
2 . 高斯是德国著名的数学家,近代数学奠基者之一,享有“数学王子”的称号,用其名字命名的“高斯函数”为:设
,用
表示不超过x的最大整数,则
称为高斯函数,例如:
,
.已知函数
,则关于函数
的结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7179c645736d68c90023f83d7f11ed01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797715acd30d07aabbed52bd10b234e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a6c086cd67c729ec094c21c0d45a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602c6c52cae281dc7dad9bc7cc07d6bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() ![]() | B.![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,
.
(1)当
时,求函数
的值域;
(2)设函数
,若对任意
,存在
,使得
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e11986f2037619f9482571b2772bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae4c6625e8245ead542e6fcb66b048d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b87ee1c9b52047aa8f78de4e8c658c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aac9b408a0111a88df4fbc36dfaf054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12cb0f74068a55559864064806e9bb98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba17f85b7a7746fd6e6f5a276e453a.png)
您最近一年使用:0次
2024-03-04更新
|
361次组卷
|
2卷引用:安徽省宣城市2023-2024学年高一上学期1月期末数学试题
4 . 已知函数
.
(1)若
,且
图象关于
对称,求实数
的值;
(2)若
,
(i)方程
恰有一个实根,求实数
的取值范围;
(ii)设
,若对任意
,当
时,满足
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb49512c66fdf46280daa506f5458004.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be033199f77a8822a8514eafab5162d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f59eb2942c435d69c1e48c2c61c111.png)
(i)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e735656890d668f67f1538fe702b366a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc373640d8d66865998853b3c3f7be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71530343bd5d7121c2e77b10aff7bd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57318f5659bc916624d975b7146e8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
5 . 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,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
关于
的奇函数,给定函数
,关于
中心对称.
(1)求
的值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)已知函数
,若对任意的
,总存在
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291aaad429837ab6dc1f99b9f7327cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f4cf449b51f221f9cb26e71a9dbebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a42e14c5d826813dd33e04be2d2c26d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f5fc756bf1aa3099dba53a6caba5a8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9dccd1d5763d4c2a8799ead64f475d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee1e47231d0c468d7e2d720a0fdeee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1247c1725b0a2037e53cbf5f7a668483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af9f0245165190c43c12ab642a97a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
6 . 设
为给定的实常数,若函数
在其定义域内存在实数
,使得
成立,则称函数
为“
函数”.
(1)若函数
为“
函数”,求实数
的值;
(2)证明:函数
为“
函数”;
(3)若函数
为“
函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54bb27ea04432576f9fa34d6fc0bd971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d5408842cf8095d3b0a4e1bef10226.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0a00c98a1184c0a8f3a92610bd306b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d9232cc485aadda3d0c529eee4616f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efab890e2314c6fbebebe6341fb7879a.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f9fdfab6e5485d35bdfe7d1909c257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efab890e2314c6fbebebe6341fb7879a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
7 . 已知函数
(其中
),若关于
的方程
有四个不等的实数根,从小到大依次为
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8fc90b6273d8bc253c113ec2c2e1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2492929137a56abbdeeea4101a4b896a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 已知定义在
上的奇函数
满足
,
,且对任意
,
,都有
,又函数
,则函数
的零点个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a053c31366873abc1740437cae8c321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a229eccad85b190aa5186a434efe7769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698cf53f76a1d637dfe2732d0a866eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3752f20e4301455ca1a99768eb2ef6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
A.8 | B.9 | C.10 | D.11 |
您最近一年使用:0次
名校
解题方法
9 . 设函数
的定义域为
,
为奇函数,
为偶函数,当
时,
.若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe17821ea81c6fec60bd5273901bd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25990e1d373ac30d7480633e47cc1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b9205cf6a58cf9f9fcaab3417519f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de52485227217f25d11676b289fa5c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdff65ed9e7a2ca957f420c40a3a4cb0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-17更新
|
392次组卷
|
2卷引用:安徽省A10联盟2023-2024学年高一上学期期末检测数学试卷
10 . 已知函数
,
.
(1)若
,求函数
的值域;
(2)若对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539984081c2472e81c91e61fe87b4c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0eef90b394d3e1f7047aa8746f4f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次