名校
1 . 已知
是定义在[-4,4]上的奇函数,当
时,
.
(1)求
在[
,0)上的解析式;
(2)若存在
,使得不等式
成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc868a2077000982bd4594d95cfc351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4c1cf6eada1c02bc34602a876711eb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a11b8a2fc710d26c89953d4d3a4eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae0cf64baf5bf264f71634f504e5ae8.png)
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解题方法
2 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818cb0975aebb51293a90e5748c7c25.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a321765ddf6a5449ad4cbb8261b98cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818cb0975aebb51293a90e5748c7c25.png)
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解题方法
3 . 已知集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fc56a6cb5e7c4ee9dabe37a1355951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1244581d8afa372ebae5b4ee3faded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 函数
的单调递减区间为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef4b5f9407e0df7a17a8bc771268e57.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 已知函数
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227dc09fba78864394b65a2a425b17f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1587b6be8e16252561ae0135e579b2.png)
A.3 | B.2 | C.1 | D.0 |
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6 . 若函数
是定义在
上的减函数,则实数
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e779cc12a68bdc30ede74d93665d6a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 函数
的定义域为集合
,关于
的不等式
的解集为
,若
,则
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e713e957ad7d313c9135e3e048516313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8b241aa8eff44238efc6d199ba5471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ceb1f338fa60976229d7ec6531b626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 对数的运算性质是数学发展史上的伟大的成就.
(1)对数运算性质的推导有很多方法,请同学们推导如下的对数运算性质:如果
,且
,
,那么
;
(2)因为
,所以
的位数为
(一个自然数数位的个数,叫做位数),试判断
的位数;(注:
)
(3)围棋和魔方都是能锻炼思维的益智游戏,围棋复杂度的上限约为
,二阶魔方复杂度上限约为
,甲、乙两个同学都估算了
的近似值,甲认为是
,乙认为是
.现有一种定义:若实数
,
满足
,则称
比
接近
,试判断哪个同学的近似值更接近
,并说明理由.(注:
,
,
)
(1)对数运算性质的推导有很多方法,请同学们推导如下的对数运算性质:如果
![](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/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8905be1335a8703769b0ad90eb6b1603.png)
(2)因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debc5f7846c70bdfb5911af22b83558f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5bdc4ab4fd3f97dc0fd63038015386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295ee20e2e288c6c0ea3a54733876a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eec3c995225b61aec23e4a4e5489416.png)
(3)围棋和魔方都是能锻炼思维的益智游戏,围棋复杂度的上限约为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f610f3ed73c02ddc0fd21b34d12ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76992e26e825328ac4195cdb64e940ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57584805a70c17d752bbd0def995accc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc51142755442f117c9889e820bcebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3025d924b323476fcc962dc6df6c9d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b2f36a11b3ee72115629252bcdbe61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57584805a70c17d752bbd0def995accc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f4d8318aba2dd01bfdc4c6b77c6121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab1cb23df1e01a5120207dbfb4ae6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f570a51c972c385489c7d3348be1cd6.png)
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解题方法
9 . 当
时,
,
,
,
的大小关系是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64839dc7ca709f6546399dcb84141b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22cbe3b3f024664dcd8c02b25c6a24c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883e58ed061e7d1dfd98d05408ac156a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf7e90fae3cbe8649b31fabdde6f63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e225a138f6611d48a8582e2f561ec048.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
10 . 若3a+2b=2,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8158e8ba84ee493205bb2981867cd861.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8158e8ba84ee493205bb2981867cd861.png)
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