已知函数
当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2903dddcf3c354c179bc9f8bb8b4d168.png)
(1)若
,求
的值;
(2)求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e3b738c934b707e167737bf455bd9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2849c7926b09a43804c63473b65347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2903dddcf3c354c179bc9f8bb8b4d168.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245985a19e6b0744248b026c29ba4b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6369cd1db768436809404b1f3c4132c0.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e3b738c934b707e167737bf455bd9f.png)
更新时间:2023-12-22 23:58:34
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解答题-证明题
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适中
(0.65)
【推荐1】定义在R上的函数
满足:对任意
,都有
,则称函数
是R上的凹函数.已知二次函数
.
(1)求证:函数
是凹函数;
(2)求
在
上的最小值
,并求出
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fc24b04012f59a9e4e5f0845e74b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7a1783349936cc7254a4a8694c6812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6090b09690819fb41379c6736363f01a.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
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【推荐2】若函数
对定义域内的每一个值
,在其定义域内都存在唯一的
,使
成立,则称该函数为“
函数”.
(1)判断定义在区间
上的函数
是否为“
函数”,并说明理由;
(2)若函数
在定义域
上是“
函数”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a206ec398c89f6c8801303ff377a0dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c08afecfeadb23d7ad746820243ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a2f20d966d1d8ffd3898fddfa4d570.png)
(1)判断定义在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fdd4e3401ce69071c91f1f068501f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d71b2afb9e2a373e2dd9601ac78ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a2f20d966d1d8ffd3898fddfa4d570.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eaee4e2b7d47a3ae79fe3772e664b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24705c61d42b941f65585ef6fb87aaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a2f20d966d1d8ffd3898fddfa4d570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b826b311d92bcb33716286760973083f.png)
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名校
解题方法
【推荐2】已知
,
是关于
两个根,且
为第三象限角.求:
(1)
的值;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a8682ce516ee97ac5d95a1bc1c30c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17cac1632cfc117087aa7fc1569a8f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9810a06a3e2cf2c01df749e4666ac1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85572144f512da6bbb42070df5f4cd75.png)
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解题方法
【推荐1】已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d780c08609c10b3fd00c45ca3573507.png)
(1)求
的值;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d780c08609c10b3fd00c45ca3573507.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b55c9a3c2eb8322fff7aca0502960c7.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd14a0e04f74359313206c17a91e35a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e133f1d0ff8e90b219f6f779aedd0b.png)
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【推荐2】设i为虚数单位,n为正整数,
.
(1)观察
,
,
,…猜测:
(直接写出结果);
(2)若复数
,利用(1)的结论计算
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f687593cb4ecef31667bf2320fdfe000.png)
(1)观察
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fedebd42a72b78551a9184bdc62f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e234081bf48fe337f9b9e3db4410041b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91792453acf1e0205df1732fc224971f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7adcf88890c9fec6cfb37bfe7a6fe4.png)
(2)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57a596bcee5bbe4aeb6805f7a4a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585b706595c3f0ad6ecec5ea9d130e36.png)
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解题方法
【推荐1】已知向量
,
,
.
(1)求
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(2)在
中,内角
,
,
所对的边分别为
,
,
,且满足
,
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab75437fa2244049ddb8028d3154e7d.png)
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(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8226c4b022ee229534a84511217e69a.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
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【推荐2】后疫情时代,很多地方尝试开放夜市地摊经济,多个城市也放宽了对摆摊的限制.某商场经营者也顺应潮流准备在商场门前摆地摊.已知该商场门前是一块扇形区域,拟对这块扇形空地进行改造.如图所示,平行四边形OMPN区域为顾客的休息区域,阴影区域为“摆地摊”区域,点
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和点
分别在线段
和线段
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,
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(1)请写出顾客的休息区域OMPN的面积S关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e06ca53803f042a5eca99f56a70f05e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46a45b12c2acb4f377e29295640a2e1.png)
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【推荐3】已知函数
,函数
与函数
的图象关于原点对称.
(1)求
的解析式;
(2)求函数
在
上的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66fe0c69dd84c27a54095dac38a641.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)求
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(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3aae9c8988f4a48db69cad3308942c9.png)
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