名校
1 . 已知函数
是偶函数
(1)求a的值;
(2)若函数
的图像与函数
的图像没有交点,求实数b的取值范围;
(3)若函数
,
是否存在实数k使得
的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c4c1150e58f5fc9b9ad5d4b04f07fb.png)
(1)求a的值;
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0d06245241dc3d1d673af1f5990e5f.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6968b2a782093a022764cda7b3c8a497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7758c571ee31edfbd528ada5c822c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
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名校
2 . 已知函数
为偶函数.
(1)求k的值;
(2)若方程
有且只有一个根,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b7fe81461bbd1fedcb4cf79d48b3a4.png)
(1)求k的值;
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b9c135f19f8a508988216438e93538.png)
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3 . 已知函数
在区间
上有最大值4和最小值1.
(1)求
的值;
(2)若方程
有两个不相等的实数根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe68d9c97f8e8fb173848363160ba79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44284ff1ea50429a0610e13363be6080.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77d5b194fbd4e6295985b95747312ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
4 . 已知函数
且
.
(1)若
,求不等式
的解集;
(2)若
,是否存在
,使得
在区间
上的值域是
,若存在,求实数
的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad169cd4a58889907f54f04707b59fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1ebc40126e8670e98e25c50f042511.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493a0cd10d3d0399173c04163740a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e799e937076aa5a7dcd51cdc0f40f6b0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e310653f87fe78a5ec8b87f205fa1635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70657d6c50f59adc8fe76dcd35de8bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa208c8bab34df3e76f87552abc985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182930dfaf54db6d4beefeee7e3b82cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
5 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68a27d247573941f2fd9a88ddd77438.png)
(1)当
时,对
恒成立,求m的取值范围;
(2)若函数
在
时有两个零点,求两个零点之间距离的最小值,并求此时a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68a27d247573941f2fd9a88ddd77438.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e2fa1f4e3b10324a455e348d0676480.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c77befb23ddbca57b9c341f5b9412e.png)
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6 . 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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名校
7 . 已知函数
.
(1)若
,求关于x的不等式
的解集;
(2)若
,且方程
有两个不相等的负根,求实数b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75d0c3b10fd1890e1afcd9886c73b99.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef2635c6e599f816c706e471a3c197d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc478be171c125e452496ae2bf4ccb3c.png)
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解题方法
8 . 已知函数
的定义域为
.
(1)求
的取值范围;
(2)若
,
,当
时,函数
在
上的值域为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0bdf82731fc14741d596662b8ae2d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876c4da096be1ab01fcd25fdabe6bba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390ff951abd64fc3f9e56bed2a8f3c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ad243c53cfa65aa601ab7eb9141168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd8466b576ad34d6ef492599940f4b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd8466b576ad34d6ef492599940f4b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9 . 已知函数
且
过定点
,且点
在函数
的图象上.
(1)求函数
的解析式;
(2)若定义在
上的函数
恰有一个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbc41ba647a7774b168ca21ed05ee9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03373ea8b1ba832b962fca109769ec4f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5f4dd21b7cb605a33c565b40fb9898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
10 . 已知函数
是偶函数.
(1)求
的值;
(2)设函数
,若不等式
对任意的
恒成立.求实数
的取值范围;
(3)设
,当
为何值时,关于
的方程
有实根?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03ccc88d04a783c702dfac8fc0a446b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00a33a4791c38fadf562929b2595ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527a896aec4a245945e5edee00deed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63afeacfbd60ac052fa91a5cb47d1f40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1752aaf32fa06ca15a3c465ffe5e7c.png)
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