名校
1 . 已知函数
定义在
上且满足下列两个条件:①对
,有
,②当
时,有
.
(1)求
,并证明函数
在
上为奇函数;
(2)判断
的单调性,并证明;
(3)若
,试求函数
的零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1684ce79f1760a4e0b820e3c4c1822f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ce23d4f9f61a8b1f99d11f4cd2c1d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fc57f4827b2985a659d91e9ebafbef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f3d2696aed6a4752b7bcc1368f073d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9a6b41e25a901542209ab07a957290.png)
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名校
2 . 已知:
是
上的奇函数
(1)求
的值;
(2)判断
的单调性,并证明;
(3)设关于
的函数
且
,使得
.求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c00f5b7df36dd6f58a384f65346c00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196b07fe2c22c854a9a14c8dbdcf862a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07487b63106bdbb2388d0cc5b66a269e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1f6026ee2623513343c2b750110292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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3 . 2020年初,新冠肺炎疫情袭击全国,某村施行了“封村”行动.村卫生室为了更好的服务于村民,每天对村民进行检测和提供消毒物品,需建造一间底面面积为
的背面靠墙的长方体小房作临时的供给检测站.由于地理位置的限制,房子侧面的长度x不得超过
房屋正面的造价为400元
,房屋侧面的造价为150元
,屋顶和地面的造价费用合计为5800元,如果墙高为4m,且不计房屋背面的费用.
(1)把房子的造价表示成x的函数;
(2)当侧面的长度为多少时,总造价最低
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1dc5ee495dfc11a9c739802d77b9c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ed8461c3bea619d0f53e9abc2deb7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffacf08ca6f494cfdf030719136692a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffacf08ca6f494cfdf030719136692a.png)
(1)把房子的造价表示成x的函数;
(2)当侧面的长度为多少时,总造价最低
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4 . 计算求值:
(1)
;
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b0403b2c5b96cb7746ad442897b046.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe8e8c5028f0f85878233c44be1bb8a.png)
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5 . 设全集为R,
,求
及
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33a013c10ecd106bd275619917b4e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e26031c3503a7feaed656c48614fc52.png)
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解题方法
6 . 已知函数
,
(1)求
;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5be34aa951af1b06de02c1bad4754.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748ea8201812d469291017e2104c9bc2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d0e60653e1358ed661fd6ed66b6403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9786c92b53010f3722ad0b7eae513c41.png)
,
.
(1)判断并证明函数
的奇偶性;
(2)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9786c92b53010f3722ad0b7eae513c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa60005db7cca8485d551460eb835bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c85886dad735d5b8048ba3d3eab4ce4.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e5be7e6785730b3c109a8a1354f319.png)
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名校
8 . 已知函数
.
(1)当
时,求
的定义域和单调区间;
(2)若
在
内为单调函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215afbdd36625e77365c77ef8962800c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
9 . 设集合
,
.
(1)若
,求
,
;
(2)若
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0b7a03ab1777e604dd32d98af2c648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e409f6b9d40225e4604eb8058b7ff0d1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36107591b80216ded064f86af687b43.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9d50619b779c1056602f46b2a95e90.png)
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3卷引用:安徽省滁州市六校2020-2021学年高一上学期调研考试数学试题
安徽省滁州市六校2020-2021学年高一上学期调研考试数学试题湖南省郴州市嘉禾县第一中学2020-2021学年高一上学期第四次月考数学试题(已下线)第03讲 集合的基本运算(考点讲解+分层训练)-2021-2022学年高一数学考点专项训练(人教A版2019必修第一册)
10 . 化简
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5898b1eea037310ec98b0cf2d56fb24b.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5898b1eea037310ec98b0cf2d56fb24b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d04f2c857b17bc7e5d1f46650dd6c2.png)
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