1 . 对于定义域为D的函数
,如果存在区间
,同时满足:①
在
内是单调函数;②当定义域是
时,
的值域也是
.则称
是该函数的“和谐区间”.
(1)证明:
是函数
=
的一个“和谐区间”.
(2)求证:函数
不存在“和谐区间”.
(3)已知:函数
(
R,
)有“和谐区间”
,当
变化时,求出
的最大值.
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/85788af6b4a64af49a2488b14790cbc4.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/0c9cc65ece4c41f7932a390bb4a491c1.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/86162c78c4b144bc89a2c748a040b308.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/5bfa40ca62b848a4b0515b76807276ec.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/5bfa40ca62b848a4b0515b76807276ec.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/86162c78c4b144bc89a2c748a040b308.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/5bfa40ca62b848a4b0515b76807276ec.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/5bfa40ca62b848a4b0515b76807276ec.png)
(1)证明:
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/f237254e258b4ec281e12610b5d7e5ab.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/85788af6b4a64af49a2488b14790cbc4.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/63c0d3e3823644e5bbe2efe41ffe1590.png)
(2)求证:函数
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/860a31536a6b4cbba385cb94a18d53cf.png)
(3)已知:函数
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/903023ddba954478acf160b661848db1.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/80ca0bb0234f4b819f857dd8814e6fa2.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/5b6cb3b1916a44acbeee023fcd25fee7.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/5bfa40ca62b848a4b0515b76807276ec.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/931f1a47f3fd41e6bd63d40181e59177.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573182759813120/1573182766161920/STEM/036270e93bff4c29880b98c7701723d3.png)
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2 . 已知函数f(x)=ax2+bx+c,满足f(1)=﹣
,且3a>2c>2b.
(1)求证:a>0时,
的取值范围;
(2)证明函数f(x)在区间(0,2)内至少有一个零点;
(3)设x1,x2是函数f(x)的两个零点,求|x1﹣x2|的取值范围.
![](https://img.xkw.com/dksih/QBM/2016/2/25/1572499519602688/1572499525263360/STEM/5a6a3fa3186f4c6ba505479aba7bd74b.png)
(1)求证:a>0时,
![](https://img.xkw.com/dksih/QBM/2016/2/25/1572499519602688/1572499525263360/STEM/eb7c214e6c194b48986eba5c20d294d0.png)
(2)证明函数f(x)在区间(0,2)内至少有一个零点;
(3)设x1,x2是函数f(x)的两个零点,求|x1﹣x2|的取值范围.
您最近一年使用:0次
2010·吉林·一模
3 . 已知函数
(Ⅰ)求证:对于
的定义域内的任意两个实数
,都有
;(Ⅱ)判断
的奇偶性,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c71f2109a6715a12a16fb0e4aee29b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db48ca9fe7c14d17493fa4a4333aa273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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11-12高一上·北京·期中
解题方法
4 . 设函数
的定义域是
,对于任意实数
、
,恒有
,且当
时,
.
(1)若
,求
的值;
(2)求证:
,且当
时,有
;
(3)判断
在
上的单调性,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b75d15ed45e8112211198215d04629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be4ab7d32ed15c176c550d8543ab369.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e817f37f5a814e856ebc4a16d676ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbaf18319364db23f555536976267e9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
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10-11高一上·江苏南通·期中
5 . 已知函数
.
(1)判断并证明
的奇偶性;
(2)求证:
;
(3)已知a,b∈(-1,1),且
,
,求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319537d01e112733378c7db0c9f97c07.png)
(1)判断并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db48ca9fe7c14d17493fa4a4333aa273.png)
(3)已知a,b∈(-1,1),且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c083bdb6c8f679ae479e3b0c405abff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79b135e345c4ec69529c86a7726f6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3bf2007903adc64d089a054c2284a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4889b4b46d3cd6dd677d200bdf4914fe.png)
您最近一年使用:0次
2016-12-01更新
|
1255次组卷
|
5卷引用:2010年江苏省南通市高一上学期期中考试数学试卷
(已下线)2010年江苏省南通市高一上学期期中考试数学试卷(已下线)2011-2012学年江苏省扬州中学高二下学期期中考试文科数学试卷2015-2016学年广东广州执信中学高一上学期期中数学试卷人教A版(2019) 必修第一册 必杀技 第四章 专题3指数函数、对数函数吉林省洮南市第一中学2020-2021学年高一上学期第三次月考数学(文)试题
11-12高二·广东·阶段练习
解题方法
6 . 已知定义在R上的函数
对任意
R 都有
,且当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)求证:
为奇函数;
(2)判断
在R上的单调性,并用定义证明;
(3)若
,对任意
R恒成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058fbc27ee9654d24ebda3d9e6991266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296aba0e3514cce0478cd3b6ec0e8549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44c45ef0334070fc149b452dee26ae5.png)
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10-11高三·广东·期中
7 . 已知函数:
且
.
(1)证明:
+
+2=0对定义域内的所有
都成立;
(2)当
的定义域为
时,求证:
的值域为
;
(3)若
,函数
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e207bf936f3b0cf7b3757a97c337cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be748a62dfaef37d7abfec4d2a35502.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc89e3c4f8dcd8f1bd21dbccdbb782e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69b3ada8af24923589888415f4dabe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef2f9766c341bc0bd1362e8e2bd9f552.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e189dbc979fad6bf8ca03ac1388cbac0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3141a4cbf5e3e12ccca84f2d0427430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
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8 . 已知
是定义在
上的函数,若对于任意的
,都有
,且
,有
.
(1)求证:
;
(2)判断函数的奇偶性;
(3)判断函数
在
上的单调性,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edee1985afc3e01df0acef2cf1228b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd384d86840b7b158af41f56fe29c7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7fde71807463dbdfd8fce1655a5a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca88b72ac8dc9c7c137af932de90bc7.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104375baf5cef5eb92cfc7cf13b80193.png)
(2)判断函数的奇偶性;
(3)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
您最近一年使用:0次
解题方法
9 . 已知定义域为
的函数
,对任意
恒有
.
(1)求证:当
时,
.
(2)若
,恒有
,求证:
必有反函数.
(3)设
是
的反函数,求证:
在其定义域内恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29ef32d9bc2e32ef2b8639b57dc9a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25bea6d14c16f7c06e4e028f36131360.png)
(1)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad4c3cb38a5ce9b06167ce7217453d6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75efd66493102acfe77edff8fd9db97.png)
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10 . 函数
的图象经过点
,
.
(1)求函数
;
(2)设
,
,问:是否存在实数p(
),使
在区间
上是减函数,且在区间
上是增函数?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8981b3b896bc0c9ae0cb699f94c1d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2599bfa462c966a4988436b8c8bb7b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e48e58aca82f136d6f0cc5251fd2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff43a92f35dd115e3f8a3f2dd973b7a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7be8524456ba4e9abb973da323c0c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27df58608819f3260cededaf16eb9770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d156bb96e4a831d3f7c6e338a7cbfd0.png)
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