名校
解题方法
1 . 已知函数
,且
的反函数为
.
(1)求
的值;
(2)若函数
,问:
是否存在零点,若存在,请求出零点及相应实数
的取值范围:若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8329421d27b154c453428c17a9d12c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2dc203b83eaac560bbbb006270cf5e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381d82d70f394f08451524af6e06754b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee15b93bbb09844a05dc3b8e6cb477e.png)
(1)求
的反函数;
(2)若
,求a的值.
(3)如何作出满足(2)中条件的
的图像
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee15b93bbb09844a05dc3b8e6cb477e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1898d199495e99fa697fd6eaef5020.png)
(3)如何作出满足(2)中条件的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135bcf6d7f7c04641823b90f1d038eee.png)
您最近一年使用:0次
2023高一上·上海·专题练习
解题方法
3 . 设点
即在函数
的图象上,又在它的反函数
的图像上.
(1)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
(2)证明
在其定义域上是减函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a117693f0d551e727f7ab78dd813abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
您最近一年使用:0次
2023高一上·上海·专题练习
4 . 求函数
的反函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f86d8967ac85000c7032ac9fa1f2e2.png)
您最近一年使用:0次
名校
解题方法
5 . 设函数
(其中
且
).
(1)求函数
的解析式;
(2)设函数
,
,如果当
时,
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1d41756645d0fa77bdc9355d142c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae018fde08edf0539089f98c17e11ff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a64103561364ac4c9460a72c9e154bb.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c830ce2ca4af8852ae02619139d1ad.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0fe51dd1b8af4bf8d34915791f5d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55580afa9f81ea2aea0a715ef6c4fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e91918cd4071cab9503b506c0132086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8133b8c1ed319ddea252b146e9243952.png)
您最近一年使用:0次
名校
6 . 已知
,
(1)求
的反函数
;
(2)已知
,若
,使得
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362bfce584209628bc4ad3f23e3d7b11.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae335c2e7164fd5e7e080bf559ac7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a68662a8c066193084d6e10d250d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c05daed1c965caf345bf9556068e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/283ab3c9dedec97f9c711d5e80072e7d.png)
您最近一年使用:0次
2023-12-30更新
|
547次组卷
|
2卷引用:辽宁省沈阳市辽宁省实验中学2023-2024学年高一上学期12月月考数学试题
名校
7 . 已知对数函数
的图象经过点
.
(1)求不等式
的解集;
(2)已知函数
的反函数为
,
,求
在
上的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01558dd579823e3922eca7415da543c2.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54abf5b38608a181dec9b1a105d2ff7e.png)
(2)已知函数
![](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/263ac6a453e47af2e6e0efa3ab8b4c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
您最近一年使用:0次
2023-12-25更新
|
235次组卷
|
2卷引用:云南省大理白族自治州民族中学2023-2024学年高一上学期12月月考数学试题
名校
8 . 若函数
,函数
与函数
图象关于
对称,则
的单调减区间是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b92c365582b2fcb997568cd4a1b97a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438ceb10b0331f38ccc4eb68f7987b1d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 设
,已知函数
.
(1)当
时,用定义证明
是
上的严格增函数;
(2)若定义在
上的奇函数
满足当
时,
,求
在区间
上的反函数
;
(3)对于(2)中的
,若关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2476c8c0ae7946c94c3f2e401677e7f4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b2798c6a26d02c5d2c8b1355c8c30.png)
(2)若定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966d9dd819cba29980da3700422c2497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d1a94ea3c278c2197572cc1b7725b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1c92c42188e3b2cb800d1186eab12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
(3)对于(2)中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352fdc419e6b6b9eb5bfc24dde2eb965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-12-06更新
|
144次组卷
|
6卷引用:江苏省南京市第二十九中学2022-2023学年高一下学期2月期初考试数学试题
江苏省南京市第二十九中学2022-2023学年高一下学期2月期初考试数学试题江西省遂川中学2022-2023学年高一上学期期末考试数学试题(已下线)5.4 反函数-数学同步精品课堂(沪教版2020必修第一册)(已下线)单元高难问题03函数恒成立问题和存在性问题-【倍速学习法】(沪教版2020必修第一册)(已下线)专题16反函数-【倍速学习法】(沪教版2020必修第一册)上海市复旦大学附属中学2021-2022学年高一上学期期末数学试题
名校
解题方法
10 . 已知函数
,且
与函数
互为反函数.
(1)若
的图象过点
,解不等式:
;
(2)在(1)的条件下,若对于任意
,都有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ede877f4dfa6b0a9a4c2e749e8fc27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081cd41dab0f2a8f84b0e9f1df4843fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54be9f6467a93e5dbd53d458fe730a3.png)
(2)在(1)的条件下,若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8182356e4323a4dfe5ceb83caf347cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cd38c1c5561866cca19ef960e979bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次