名校
解题方法
1 . 若函数
对定义域内的每一个值
,在其定义域内都存在唯一的
,使
成立,则称该函数为“和一函数”.
(1)判断定义在区间
上的函数
是否为“和一函数”,并说明理由;
(2)若函数
在定义域
上是“和一函数”.
①求
的值;
②求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abea75a25495fc2a9637c818e9392eec.png)
(1)判断定义在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d45793b96fcc2aa90c8555b1c5157af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ede389b43c78417912542746d91d00.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518f497d350fef9331d7082b09b0b9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4350514c24acc1943867a341199725d1.png)
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名校
解题方法
2 . 设函数
的定义域为
,且满足
,则不等式
的解集是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc4679a8360516b33a3cb9e86ab25b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390c620c0fd4a2cd8622171bdaf05f5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ec6c59e1ce704a29d76726e2674129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd1f61519643b2a62367079f19c6c22.png)
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名校
3 . 设数列
,
满足
,
,则下列函数
使得
,
有相等的项的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695950fe16f7972182bd2d0864e12feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a1ac9c1ab5322bb7ba6e0ec095b43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
4 . 已知函数
,
.
(1)求函数
在区间
上的最小值;
(2)若函数
,且
的图象与
的图象有3个不同的交点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1462a1906c6bc21913902ea0e4a7ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49723fcae368064d6e4d44fa4bad1ae4.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e694d52a084565a4cc3d689d4a32e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b58435e488fb30016f2109f4ff060b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203dba0b34d75467e6a0d283d29f5ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f4ab890a5f38debf3a5ceb1648ed1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024-01-24更新
|
272次组卷
|
2卷引用:四川省德阳市第五中学2023-2024学年高一下学期4月月考数学试题
名校
解题方法
5 . 已知
,则
的值域是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39444ac4ccb3e443011ccc54a922e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10866c929435c223ef0bfaadb57bad75.png)
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名校
解题方法
6 . 下列不等式中正确的是( )
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2024-01-13更新
|
299次组卷
|
2卷引用:河南省焦作市第一中学2022-2023学年高二下学期4月模拟检测数学试题
名校
7 . 已知函数
.
(1)若
,求方程
的解集;
(2)若函数
的最小值为
,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10dda958e0a26731d73c3127f9ad484.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f9a575fc639253a8efe28ab73a985e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a711a0b8c90ec23b7d449c0709746cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e35f76e01c3979ae5987f7729f9856.png)
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2024·全国·模拟预测
解题方法
8 . 设函数
的定义域为
,
为奇函数,
为偶函数,且当
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3237922154babd3021e091d185e3be.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d7661d3fc28f785b438ad8c8f9d240a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2215ece47e22ff5f4ae6fa8f77fe1636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3237922154babd3021e091d185e3be.png)
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名校
解题方法
9 . 函数
的部分图象大致为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd47ccaa266cd4e738424423f7996032.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
10 . 已知函数
.
(1)当
时,求该函数的值域;
(2)若
对于
恒成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ee55add803bf1b64b580d078cae20b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0a85351d1433071b7e7bd11eaaba85.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb48cabb2ca42afe6e3e3d09db6385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3368388525e30cb7179909b03184eb.png)
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