1 . 设集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7bb675b0ef0ec120a227f904e7e820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6bf1d26f283219879cc0bfb21526151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe156c10c39e5214f325ce8a2180858.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 定义二元函数
,同时满足:①
;②
;③
三个条件.
(1)求
的值;
(2)求
的解析式;
(3)若
.比较
与0的大小关系,并说明理由.
附:参考公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1234f123ff32cf38037649c3ff329d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a4141252d1d5410adc4da9a3e631b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ffece531ce82696c0920238efdeb113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/430d72f73ef24e73a937893c26c5c854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f095fc2b6b7eb7ecdbff0a1e78dcf9b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee684bc0ac2a74bd0fb714e94245070f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad1be9af99aa2fb00f2de6a215cf1ad.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3264fcf8cfd754947a33aff79ea9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
附:参考公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1234f123ff32cf38037649c3ff329d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b320170303e3310f9c8bb29e17d716.png)
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3 . 已知集合
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431212aa7d769932f012f3bb33ca2316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
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名校
4 . 已知
为坐标原点,对于函数
,称向量
为函数
的相伴特征向量,同时称函数
为向量
的相伴函数.
(1)记向量
的相伴函数为
,求当
且
时,
的值;
(2)设函数
,试求
的相伴特征向量
,并求出与
共线的单位向量;
(3)已知
,
,
为
的相伴特征向量,
,请问在
的图象上是否存在一点
,使得
.若存在,求出
点坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66655b7a6825b124ce596197bf2aa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(1)记向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffe91c3b3290e5eb048b0028b0a5686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6197fc9360bc260883f303f344dce62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f5a04aef63712bb14cd11854ab79b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8c56d09485b718a85ed23f637e2d77.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bda80f584d122194e5da3ab8445320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd9c7231464c17b412d8ee08848f095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25953bf09041ebbd17e08f8bd243c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8995dd0d46aa3505185b312b37d2654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc45ae56d0d739339059deff9106093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d0f698f257914921dae5b31f9051e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661249bf6499017f9e5e03db3fcd93d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b929fe0f9c13dd6dfabca91a1a4aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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5 . 已知函数
具有以下的性质:对于任意实数
和
,都有
,则以下选项中,不可能是
值的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.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/9e2469a3ff9552ad17fa8cf8b54b6d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
A.![]() | B.![]() | C.0 | D.1 |
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6 . 函数
的部分图像大致为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f8a0ac91ca429f7cf530a2b5b4e9865.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
7 . 已知
,则
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fca7650a92df37b47af88b6532783c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
8 . 已知函数
,若
,且
,则下面结论错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ba6d93a671ca21730facc7fbf052c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
9 . 已知函数
的定义域为
是偶函数,
是奇函数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea829a3414301203ddf659b0a7a5136b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b523e27f332f8591fd49bc6d7a4c05.png)
A.![]() |
B.![]() |
C.![]() |
D.不等式![]() ![]() |
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真题
10 . 若
.
(1)
过
,求
的解集;
(2)存在
使得
成等差数列,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b04f2b67e3c95a11d844e3d54e8504.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081cd41dab0f2a8f84b0e9f1df4843fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c25db143eb14b7b6997047aa3cca12.png)
(2)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e47518677c6d5041e3741d83701320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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