1 . 我们熟悉的网络新词,有“yyds”、“内卷”、“躺平”等,定义方程
的实数根
叫做函数
的“躺平点”.若函数
,
,
的“躺平点”分别为
,
,
,则
,
,
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be943c6bb7e170907c93eae6b13a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d997e3fd54416a529c5095523bc15e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17c20662a07a25d11f33a4488e31cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13487a3c7d84a5638de224a370910012.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/071a7e733d466949ac935b4b8ee8d183.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/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 对任意
,不等式
恒成立,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45256bc50846ff052fd5621be50972c.png)
A. ![]() | B.![]() |
C.![]() | D.![]() |
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3 . 设定义在
上的函数
与
,若
,
,且
为奇函数,设
的导函数为
,则下列说法中一定正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](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/ef6cbd64291fa53ffec2592a50559e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0435c98002ba4deb90636b864e5a822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6d578f9c98ce402d4cf6e4a23281c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
A.![]() | B.函数![]() ![]() |
C.![]() | D.点![]() ![]() ![]() |
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4 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b7fd83b2f31ff033b9b7c30011f4b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 已知函数
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d3a5fb665e5dc0abdb52890e4affbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281906e45b2cccc16408090c97c00c76.png)
A.1 | B.![]() | C.2 | D.![]() |
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6 . 设函数
的定义域为
,且满足
,
,当
时,
,下列结论:
①
;
②当
时,
的取值范围为
;
③
为奇函数;
④方程
仅有6个不同实数解.
其中正确的个数是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acb74208dcbe73fd8cbd89bf86bd69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645d75ed821e2cae930b5433c27c5f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1356529b99240cf586a0ee624be73c99.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4770abbde4102605920fefe983535ae.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d44ac5cb478916f81ef2d42911258aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50188f84f379b3d0418c54cbade7d7.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e57fd4660ebab6bd1dfb11329036e6.png)
④方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a73690a5521b20bb48807aff002933.png)
其中正确的个数是( ).
A.1 | B.2 | C.3 | D.4 |
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7 . 已知函数
.
(1)若
的单调递减区间是
,求a的值.
(2)若关于x的不等式
的解集为
,求不等式
的解集;
(3)若
,求关于x的不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137f95a216a91c5d249b7efada410121.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be381da62d4a042476aa11dbd5824e8d.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881fe2df23c5a0fe1d1fecbe9ffa55fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fd9965603fe4f2bc75102af9136774.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
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解题方法
8 . (1)已知函数
,求函数
的解析式.
(2)已知
是二次函数,且
,求
的解析式.
(3)已知函数
满足
,求
的解析式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2584acf4f606da6d0d2f800764c204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b52265a268ea0d46a816309b91bd3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7969bb5803ad5cd7e0bf032c85efd649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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9 . 定义在R上的函数
满足
,且
,
①
的值域为
; ②
的最小正周期是4;
③当
时,
; ④方程
恰有4个实数解.
上述正确命题的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac67215b94c77be50360a64b16cceeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5448a19cf9cf7970ffb209d5e9ffa267.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb2f360028740b06001ab1c3739c1fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350cbd2f5a3f5e72d5f0db5bd63964ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bf4aa648b06d0a9f4782bcd0821d4c.png)
上述正确命题的序号是
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10 . 给定函数
,
,对于
,用
表示
,
中的较小者,记为
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7343e8f9118952329c5c1072caa9b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809a343cb6675bdecdaf348dcdcec099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3859cd3de4d6d485df050b0f5321d6c6.png)
![](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/f7ec451b88cfb21d69e12c7fedcd9f8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3859cd3de4d6d485df050b0f5321d6c6.png)
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