名校
解题方法
1 . 定义域为
的函数
满足
,
,且
时,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9da4fdfdddc259dcef9fdd4b826b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
A.![]() | B.![]() ![]() |
C.![]() | D.不等式![]() ![]() |
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名校
解题方法
2 . 已知
的定义域为
,且
恒成立.
(1)求
的值;
(2)试判断
的单调性,并用定义证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae3a16b9fab158f4d46ff236860d39e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cb3110d75667298a8173aee405a017.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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名校
解题方法
3 . 已知函数
是定义域上的奇函数,且
.
(1)判断并证明函数
在
上的单调性;
(2)令函数
,若对
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec891bf06e4df7ba161bd6ec24205a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d755fa52c87ccaf34674c18a3f4505f8.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
(2)令函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3745f8df5000ef458bb6cb193734eac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0810990931ead519c27c1278bcaa0ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f254f2d4b70cdcdcd9a7f8ef205813df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
4 . 已知函数
满足:任意给定
,都有
,且任意
,
,
,则下列结论正确的题号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9a7e92b379b93bca9b4f7b032fb61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e70db4fa015a8b4fb6da18c6959ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae5ef85731cd913804b8ea86de3df23.png)
A.![]() | B.任意给定![]() ![]() |
C.![]() | D.若![]() ![]() |
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名校
5 . 已知函数
,
,若对于
,
,使得
成立,则实数m的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e1c34e767abf34e4e1c1a4e41877ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1faeb99a9feb18755cb3c6ad6b169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd808e2b9846b09bbe9e67bfd82fc0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad3e902bdc48a4e6042deb26c2399f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a97223e0fdac3818c661c89dfa8c441f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
6 . 已知函数
,
.
(1)判断函数
的奇偶性;
(2)用定义法证明:函数
在
上单调递增;
(3)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d689069bc1f9742b3fca3d69e55406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d4a4d94615e427e4e78061000d5e9d.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用定义法证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4af6e43343b5e4ebe27c9cb2c09fe1.png)
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名校
解题方法
7 . 悬链线
指的是一种曲线,指两端固定的一条(粗细与质量分布)均匀,柔软(不能伸长)的链条,在重力的作用下所具有的曲线形状,适当选择坐标系后,悬链线的方程是一个双曲余弦函数,其解析式为
,与之对应的函数
称为双曲正弦函数,令
.
(1)判断
的奇偶性和单调性,并说明理由;
(2)若关于x的方程
在
上有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a3ce2f0d176db995be7c9a771dd344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebc77f161714e1a05b7a10bce9f9fcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5327e5ac13899357a14c4cd68af054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333e2bc74aafdd1775f61702119b3823.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f86611c0b359282b77acac0208b6ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f0d71fab2982934bc3b223c159f98d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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8 . 已知函数
.
(1)求证函数
为奇函数;
(2)判断
在区间
上的单调性,并用定义进行证明;
(3)求
在区间[2,6]上的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47b2d73a4858fe5a169a0964c7e878e.png)
(1)求证函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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解题方法
9 . 下列函数中定义域为
,
,当
时,都有
的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ba6d93a671ca21730facc7fbf052c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580c300d1699fc2145c914a0c99ae585.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知函数
.
(1)用定义法证明
是减函数;
(2)解关于t的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdafd96f3833e55601943361fa71710.png)
(1)用定义法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)解关于t的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e34b9cbb63f8745e64d90919ae6cee.png)
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