1 . 已知函数
满足
,函数
.
(1)求函数
的解析式;
(2)若不等式
在
上恒成立,求实数
的取值范围;
(3)若关于
的方程
有四个不同的实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45717d939afd817d3378ef356d29aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a9ee90f86f252dd48868d94f4c564a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f1279d1afe86edd9a61fde66cbec01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025efb915cc19078215ecbd4776b7f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
2 . 已知函数
,函数
的一个零点为a,
的一个零点为b,则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5bfe9f9c88e86e1739b97da9a9829b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be87998faa583333a1a0aa987567f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cccdc07845d9b197e6b265f10fcb06d5.png)
A.![]() ![]() ![]() |
B.![]() |
C.![]() |
D.![]() |
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名校
解题方法
3 . 已知函数
的定义域均为
,
,
,
,且当
时.
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aba44580b708b657990ee5ace7397d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba05a18bead4c2ca2b469e8bacccf4c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af51eadf065755b7bcc4c2086f0d208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04beea76c59a6c5b096d8c5a3b77f8a9.png)
A.![]() |
B.![]() |
C.函数![]() ![]() |
D.方程![]() |
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名校
4 . 已知函数
对任意的
满足
,且当
时,
.若函数
有4个零点,则实数a的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851eae00e3369068e33a7e6420483883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95917fe23c253088f51205ad14094a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a79d7f73b6128650bf7aed538260c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b79f63d32d084bd76dc24ae164c982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f88f446bed167e2fb55f51f649af5c.png)
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名校
5 . 已知函数
有3个不同的零点
,且
.
(1)求实数
的取值范围;
(2)若存在
,使不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858a730ebeabd511374d81324b0e49b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db1ee2fbe9bcc2654ce9482b5a39a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6 . 已知函数
.
(1)若
,且
图象关于
对称,求实数
的值;
(2)若
,
(i)方程
恰有一个实根,求实数
的取值范围;
(ii)设
,若对任意
,当
时,满足
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb49512c66fdf46280daa506f5458004.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be033199f77a8822a8514eafab5162d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f59eb2942c435d69c1e48c2c61c111.png)
(i)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e735656890d668f67f1538fe702b366a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc373640d8d66865998853b3c3f7be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71530343bd5d7121c2e77b10aff7bd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57318f5659bc916624d975b7146e8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
7 . 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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名校
8 . 已知函数
,
.
(1)若函数
,
,求
的最值;
(2)设函数
,
在区间
上连续不断,证明:函数
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edecfbf1b4e1052468d209e8f017a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dce2bfe6e1fde9265d2a07c42bbdf58.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bfb22bf37b71482bd4649852a7dacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc17049fc86f1ef6b73f8a14fc24d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f77f8111c7805e673a644b0a690dcc.png)
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9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88a1d706f453ebe641928d539a55a7b.png)
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88a1d706f453ebe641928d539a55a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d75d042a2fd6581382fef773402bd78.png)
A.![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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10 . 已知函数
.
(1)当
时,讨论
的单调性(不必给出证明);
(2)当
时,求
的值域;
(3)若存在
,
,使得
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3262fcbcec80e9a9c7303b276c25e58.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68496fb61a013863499001b4deba2054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e71b7cc594da8081cc8599f6e2c529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1d56979d28f9d065e9e9aa60f6.png)
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