名校
解题方法
1 . 已知函数
的定义域为
,函数
的值域
.
(1)求集合
和
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab6c0af7aae55a6b56c531abdc8ba4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cad75d029fbb7799e1b2458470da8bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79fa35d8994545971a6cc2f864242081.png)
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解题方法
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5492182a37d89038c162b06021ca7dd2.png)
(1)求
的定义域,并判断其奇偶性;
(2)判断函数
在
上的单调性,并用单调性的定义加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5492182a37d89038c162b06021ca7dd2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0109d06b8be2e402b5ffbb0aeb501009.png)
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3 . 已知
,我们定义函数
表示不小于x的最小整数,例如:
,
.
(1)若
,求实数x的取值范围;
(2)求函数
的值域,并求满足
的实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9322dd8f56b5f8d2c667fdf0d4a9f9aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7871245c73941aa9cc43ec0f82a00dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083e66f15f0a5b04c323f1e102fe497c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650191ce718e5660ec83029419a507ff.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c4f0e587b3039889cfb2f00af8bd2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c0e0e937249bd71d711bb09fd4b2a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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解题方法
4 . 设函数
,且
.
(1)求实数
的值及函数
的定义域;
(2)求函数
在区间
上的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9690bf8272bca78106133cae2dc36f00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17ee5f43412795671704ab0e8d0b2f5.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284d3d48054ce3ad19d29f3876dffebc.png)
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解题方法
5 . 函数
的值域为
,
的定义域为
.
(1)求
;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a586717b367d464f51434a8c260585a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd78ab6562f8e8426cf9baa16db77bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
6 . 已知函数
的定义域为集合
,集合
.
(1)若
,求
;
(2)若“
”是“
”的必要条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518dff1998542da49899871ace3ec161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255669835a81d0816b30c780927bba29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-04更新
|
525次组卷
|
3卷引用:辽宁省沈阳市2023-2024学年高一上学期期末教学质量监测(1月)数学试题
解题方法
7 . 设集合
,
.
(1)若
时,求
;
(2)若
是
的充分不必要条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1af82d7e99db8e52d7264c8d2643e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a0615c1d74e908138641562ea2584f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
8 . 已知函数
.
(1)求
的定义域;
(2)解不等式
;
(3)求
在区间
上零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9fe51ece3979215e359aed46ee43e4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f62f9988d640c4fffff6d964ddcff1.png)
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解题方法
9 . 已知函数
.
(1)求函数
的定义域;
(2)若
恒成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbe65e82d1ae1c55e25ec4f9c4c11a8.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc40b6ae5fa619a79ad2f92d4f12981.png)
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10 . 求下列函数的定义域
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813210eeb39fb832bc7f5ad15d9eeaf5.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1593ca07d053bf041a6019be826b327.png)
(3)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813210eeb39fb832bc7f5ad15d9eeaf5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1593ca07d053bf041a6019be826b327.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b113ba6d2c71eceea94cf193d4b57d.png)
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