名校
解题方法
1 . 设
,用
表示不超过
的最大整数,则
称为高斯函数.例如:
,
.已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c607a62a8c3f1a29916f8fa0b8fb7f.png)
________ ,函数
的值域为_______________ .
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7179c645736d68c90023f83d7f11ed01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a6c086cd67c729ec094c21c0d45a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d0024c22d248668a379d8dd1b84cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e6743dc8683554235543c456aa8be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c607a62a8c3f1a29916f8fa0b8fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92a5aa37427537837be7d77d51c84c6.png)
您最近一年使用:0次
解题方法
2 . 已知函数
为
上的奇函数,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0632bc67a48ee16de53fe7e19ec3328.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf1f511652eceda2749095d08612afb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0632bc67a48ee16de53fe7e19ec3328.png)
您最近一年使用:0次
名校
解题方法
3 . 函数
和
的定义域均为
,已知
为偶函数,
为奇函数,对于
,均有
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4755d367c39d8d063ad5c19d244370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22e6fa3b2261d51c56efdd4c2572365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf8ec8044e1fb0602aec9a400a72a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd9a6d2b114476f24afc2fe36eed5316.png)
A.66 | B.70 | C.74 | D.78 |
您最近一年使用:0次
名校
4 . 已知函数
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e2b7e28067d812eecd139fee7ac0eb.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/250a3b258b3470f01ea99926d8085eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8d601e83386c7ca459d15f0298dc7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e2b7e28067d812eecd139fee7ac0eb.png)
您最近一年使用:0次
5 . 已知函数
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469c36eab37e2af684c590a5bbfd1780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8748635b5b945bef4b821387c6b22b5c.png)
A.12 | B.![]() | C.28 | D.![]() |
您最近一年使用:0次
解题方法
6 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0632bc67a48ee16de53fe7e19ec3328.png)
_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c51f6500839ac3936d4947f1c0f72b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0632bc67a48ee16de53fe7e19ec3328.png)
您最近一年使用:0次
7 . 已知函数
,
分别由下表给出:
满足
的所有
的值的和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![]() | 0 | 1 | 2 | ![]() | 0 | 1 | 2 | |
![]() | 0 | 2 | 1 | ![]() | 2 | 1 | 0 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b7fe0e20871b778664e9865125df88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
解题方法
8 . 定义在
上的函数
满足对任意x,
,恒有
,且
时,有
.
(1)求
的值;
(2)证明:
为奇函数;
(3)试判断
的单调性,并加以证明.
![](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/f370a1d4dd341e5ab1774a66c66c1204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
解题方法
9 . 已知
是定义在
上的奇函数,且
,当
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83fe6062ebed72f4b3c088a8545514a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112e02bc4c05dc711e62543ff70eb984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b25472f2e834106c0747873a6e5c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83fe6062ebed72f4b3c088a8545514a.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
不过原点,且对
,满足
则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4aa0c78840d268cab45b55637edb43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8188641e38701831da7f477b9c46d908.png)
A.![]() | B.![]() |
C.若![]() ![]() | D.![]() |
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