1 . 已知①设函数
的值域是
,对于
中的每个
,若函数
在每一处
都等于它对应的
,这样的函数
叫做函数
的反函数,记作
,我们习惯记自变量为
,因此
可改成
即为原函数的反函数.易知
与
互为反函数,且
.如
的反函数是
可改写成
即为
的反函数,
与
互为反函数.②
是定义在
且取值于
的一个函数,定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c5d65e0ccd27748fcbc420c6a2e22.png)
,则称
是函数
在
上的
次迭代.例如
,则
.对于一些相对复杂的函数,为求出其
次迭代函数,我们引入如下一种关系:对于给定的函数
和
,若函数
的反函数
存在,且有
,称
与
关于
相似,记作
,其中
称为桥函数,桥函数满足以下性质:
(i)若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0e8a92152787274ed6e06a21ef1661.png)
(ii)若
为
的一个不动点,即
,则
为
的一个不动点.
(1)若函数
,求
(写出结果即可)
(2)证明:若
,则
.
(3)若函数
,求
(桥函数可选取
),若
,试选取恰当桥函数,计算
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66c24e657d998beb013ad1fb311d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f93e3581e920716e710e22b31006bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f93e3581e920716e710e22b31006bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63ced31d098cfb0cf14d906e97e6353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66c24e657d998beb013ad1fb311d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955f3c2b80eebc3f88c804112e5f41f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955f3c2b80eebc3f88c804112e5f41f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb87ce86e2c9a1a8188b03b74438fdd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb87ce86e2c9a1a8188b03b74438fdd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66c24e657d998beb013ad1fb311d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ef38135b0e7906687d8a4918a4cb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43737e3ca063dfc210d0c72924a4930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808bd2fc4b344e7669fca65b4fa122df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808bd2fc4b344e7669fca65b4fa122df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c5d65e0ccd27748fcbc420c6a2e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c110a1293773729278a214c7fe8d544e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052ddf3664af9ab2990f3ea622997e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ca4e4f009554b599eab90e1d94c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](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/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71567deb76e48f8a2424b06536cbe465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66b033ee7a03c7b3508583481465275.png)
![](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/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1249f186df944244da02e1b8c754005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1249f186df944244da02e1b8c754005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0e8a92152787274ed6e06a21ef1661.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f199ad3fad8657afa38f370b319a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192bb45bd15b200f40b34377bc58905b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1249f186df944244da02e1b8c754005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99315f5b2ae9bea18e06401b41d3780c.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becd598a11b876d858728161a7a09705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ab7717944da2b6cc305b6a65f91408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85f9d9be0ba965ff7beb0e011267f29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bee7f1ccd52c7d526b6d466b970e769.png)
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名校
2 . 三角函数的定义是:在单位圆C:
中,作一过圆心的射线与单位圆交于点P,自x轴正半轴开始逆时针旋转到达该射线时转过的角大小为θ,则P点坐标为
,转动中扫过的圆心角为θ的扇形,由圆弧面积公式和弧度角的定义,可知面积
.类似地对于双曲三角函数有这样的定义:在单位双曲线E:
中,过原点作一射线交右支于点P,该射线和x轴及双曲线围成的曲边三角形面积是
,双曲角
,则P的坐标是
.其中,
称为双曲余弦函数,
称为双曲正弦函数同样,有类似定义双曲正切函数
双曲余切函数
且有如下关系式:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d279cc5e9f902480c9a0ea810cf9d3a.png)
,
的初等函数表达式.
(Ⅰ)双曲三角函数有如下和差公式,请任选其一进行证明:
①
;
②
;
(Ⅱ)①求函数
在R上的值域;
②若对
,关于x的方程
有解,求实数a的取值范围.
类似三角函数的反函数,试研究双曲三角函数的反函数artanhx,arcothx.
(2)①证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b450e870513b9cf6021b6416959224.png)
②已知
的级数展开式为
,写出
的级数展开式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b93ac1e1087ef8a7827e22983ab895f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33074bee68ff41ba4c6b675578f19957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050c00da6d39ad0fae411836b0a26979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15cd370bd2337b78fe820b7b61438c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2dc9ac6460d3c72e915e93b9f16d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c627427318b62d977ff7a86c2cb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53b8e0108664bf39aa302570457199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1fe4e3a61667cfe81973a300859f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a252d4a56c74a8829afb1fccbe09d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0961cbc097652b999cd4106c671e4cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d279cc5e9f902480c9a0ea810cf9d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53b8e0108664bf39aa302570457199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c627427318b62d977ff7a86c2cb5.png)
(Ⅰ)双曲三角函数有如下和差公式,请任选其一进行证明:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1079114cdde9367a22632b0165f1a1a8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3510bba38a7f232cc4d9e437e78f5b6a.png)
(Ⅱ)①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e154c56d574646a2a541a3fe70c6307b.png)
②若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f2372e3d0c3de8f5f0579312efe38b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c47cddd4b31aeacfad8f81705b827.png)
类似三角函数的反函数,试研究双曲三角函数的反函数artanhx,arcothx.
(2)①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b450e870513b9cf6021b6416959224.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802ae3e64c0bb802cc83bf3cf81bfe49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1bbb717893d3adb6ce58b3a99bc257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0593e23740ebd0cd068a2eadf059e3.png)
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3 . 我们知道,函数
与
互为反函数.一般地,设A,B分别为函数
的定义域和值域,如果由函数
可解得唯一
也是一个函数(即对任意一个
,都有唯一的
与之对应),那么就称函数
是函数
的反函数,记作
.在
中,y是自变量,x是y的函数.习惯上改写成
的形式.反函数具有多种性质,如:①如果
是
的反函数,那么
也是
的反函数;②互为反函数的两个函数的图象关于直线
对称;③一个函数与它的反函数在相应区间上的单调性是一致的.
(1)已知函数
的图象在点
处的切线倾斜角为60°,求其反函数
的图象在
时的切线方程;
(2)若函数
,试求其反函数
并判断单调性;
(3)在(2)的条件下,证明:当
时,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda90af8ba1d6f9e21a49e96b709f16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7edf0a72070071cbbcd54c9e2f5ce1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ae23cf6a2823451f9676220b32c782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7edf0a72070071cbbcd54c9e2f5ce1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3fe53f7586f7cfbc17e2fd1c1a091bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3fe53f7586f7cfbc17e2fd1c1a091bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a4f23baf90cbc32cba9f6b9bfea2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135bcf6d7f7c04641823b90f1d038eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135bcf6d7f7c04641823b90f1d038eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3654254401fc902c3cb4912969f21f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135bcf6d7f7c04641823b90f1d038eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83104d98d6920b19fe2cc3cf097bce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
(3)在(2)的条件下,证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65cc52aacc31a21a443c8de0374b24f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f8c8e4cfd60c1793cfa4526d1fc853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897453f27022194d1f57e8b54960111f.png)
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24-25高一上·全国·课后作业
4 . 写出下列指数函数的反函数:
(1)
;
(2)
;
(3)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe49779f2db4a075d3241052eb87d8b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027c2fdcfaaf830eab93c84ceed173bf.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6829245aa667acd74e0dffdbc670c42b.png)
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名校
解题方法
5 . 已知函数
,函数
与
互为反函数.
(1)若函数
的值域为
,求实数
的取值范围;
(2)求证:函数
仅有1个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f56243e7c102bcea2755b9e5ab8455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6655e9e9bb9995d0c7e1dd02eb718d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1680e0b88a968543d32bb4ccf820e0d.png)
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2024-03-01更新
|
321次组卷
|
2卷引用:湖北省部分学校2023-2024学年高一上学期期末考试数学试题
名校
6 . 已知函数
,
为函数
的反函数
(1)讨论
在
上的单调性,并用定义证明;
(2)设
,求证:
有且仅有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4ccec118032fd96e0713b04c3a27a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4a2b3998705e51dbade9ada0873b2b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041f581f277a2de1ef41c354b6e6991e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d126a2ae5babaf18b9082a975cdc52.png)
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解题方法
7 . 已知函数
(
,且
),从下面两个条件中选择一个进行解答.
①
的反函数经过点
;②
的解集为
.
(1)求实数a的值;
(2)若
,
,求
的最值及对应x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a04546d92fd165fc1ad2cc82c2dbb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac7c28099bfbb7dc2a45ad166eace05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0878cff562bec40a7bd879f81e0c6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea5cf29ff47f6c64f4537c425e0967f.png)
(1)求实数a的值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e2eab4171f9c3e73b0e0a1af336cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f3fc2a6b50f762c8378283b56023f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
解题方法
8 . 已知函数
为对数函数,函数
的图象与函数
的图象关于
对称,设函数
,且对任意
都有
恒成立.
(1)求函数
的解析式;
(2)若函数
在
上的最小值为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e78f50ba34a711fe64198e358b62e0e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd84da85388fcc2b7b74eed6790b9318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f48232ea888fd31e850879c444641f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d786ee0f73092274bce83c0670d5030a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a08521c64aae3d19fe3fe1da35708f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade31f6684e3033e377b90691ec2204d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
9 . 已知指数函数
的反函数为
.
(1)求函数
的解析式;
(2)已知函数
,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babb3ff0eabe0651b43db92dcc68c11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92c21afe43b0ed71be8bcffe1983760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e35de1e842df1a7c2daa0f75a3abd1c9.png)
您最近一年使用:0次
2024-01-20更新
|
487次组卷
|
2卷引用:重庆市南开中学校2023-2024学年高一上学期期末考试数学试题
名校
解题方法
10 . 已知函数
.
(1)若方程
的两根为
与
,求
的值;
(2)设函数
,若
的最小值为1,求实数
的值;
(3)设函数
,记
为
的反函数,设函数
,当
时,
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e7c1e306fe3124dc730b2f8f681bdd.png)
(1)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124f5d03ab9692ef07f1ad6913e4b0e7.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/450398974b1561ca801e102e16df6789.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489c86eac6482ddbc9d704b0debb4c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec52b67f780fa3f0eff0197a20a17b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686a0e76d6c06d4a507e47833eaa5755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f196f6236188084f3b2c9f2b68c05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34a33d135646e1b7581ecac91fbcffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9907849f70ca76e2d5cc80b5ced07452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8380ca790c38c3ebae35965834016f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-01-20更新
|
314次组卷
|
2卷引用:辽宁省大连市2023-2024学年高一上学期期末考试数学试卷