1 . 函数
(其中
…为自然对数的底数)的反函数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf09969aa45affe19fd9514e72a0de3.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07d7af2ede4abfa4d647b4058992d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf09969aa45affe19fd9514e72a0de3.png)
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2 . 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.![]() |
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解题方法
3 . 已知函数
且
,其反函数为
.
(1)若
,求
的解析式;
(2)若函数
值域为
,求实数
的取值范围;
(3)定义:若函数
与
在区间
上均有定义,且
,恒有
,则称函数
与
是
上的“粗略逼近函数”.若函数
和
是
上的“粗略逼近函数”,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cae47ad50ac506ced900f0a5156c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019b34c028726bbf4e12fa25391d7801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)定义:若函数
![](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/d6d0023896010151f7829e462fb79c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa09bf6979429e792c82eea32a8df5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc69dd6b191f31ea8d87f867a456a4a.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/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51604543c976357c2342d733930c721a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696ab0893248236ce911cbcc7c909f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221f9c828a6de90bcae98354634a8ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
4 . 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/246de316aacce5e2a1b482840ff02f82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dbc20ccb44e28990f0ad8499dbdba22.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a31ba10aa94b7af6088d886f71adcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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5 . 已知函数
与
互为相反数,且
,函数
的定义域为
.
(1)求
的值;
(2)若
,求
的值域;
(3)若函数
的最大值为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2702a5539ca829b8b7a08407f0996e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b16f8909a04c6da49fec21bd78d609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9768c91b77d56918820e0ce3167cdd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6 . 已知函数
的图象与
的图象关于
对称,且
,函数
的定义域为
.
(1)求
的值;
(2)若函数
在
上是单调递增函数,求实数
的取值范围;
(3)若函数
的最大值为2,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2702a5539ca829b8b7a08407f0996e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9735374e92698d97184708196619ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70bd87fba9735c16f4332bf00adaa09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695d0c02fabb67cba311e4d7187324f0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695d0c02fabb67cba311e4d7187324f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2019-11-07更新
|
302次组卷
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2卷引用:湖南省常德市临澧一中2019-2020学年高一上学期段考数学试题