已知函数
是定义在R上的奇函数.
(1)求实数m的值;
(2)用单调性定义证明函数
是R上的增函数;
(3)若函数
满足
,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1467fe6e050ae4e7778c2e8f57c66c.png)
(1)求实数m的值;
(2)用单调性定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e678c73e812b5c55b663ecf81d5aa3e.png)
更新时间:2021-01-28 20:19:21
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适中
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名校
【推荐1】已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
(1)证明:
在
上单调递减,并求出其最大值与最小值:
(2)若
在
上的最大值为
,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cac46fe7735b2b1f998cbfb4372b871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c610fe31b2d5f070d5c92c69337e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7266b2ef457b8ddeee3fa2cc24022e.png)
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【推荐2】已知函数
.
(1)当
时,判断
在定义域上的单调性,并用单调性定义证明;
(2)当
时,关于x的不等式
在
上恒成立,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df600b574600724416316688dfb4e9e3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad96e7702c5af48a34bdbab0f52441c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
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解题方法
【推荐3】已知函数
的定义域为R,且
.
(1)判断
的奇偶性及
在
上的单调性,并分别用定义进行证明;
(2)若对
,
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4105adc6c72c366ec2c17de5dd25b74e.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24eb36914c5d05da7d3e23900f0b4124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6bab6de07b3df885b3aa09127f0e2bf.png)
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【推荐1】已知函数
.
(1)用定义证明函数
在
上为减函数;
(2)若
,求函数
的值域;
(3)若
,且当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103cce33d2362ec95790e24c8fe6c759.png)
(1)用定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2372f424431ce7b547a66b7d61d75421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10509279eb4f156c73ad0216d2991664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85187c85826beeca12137805293fff77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
【推荐2】已知定义域为
的函数
.
(1)判断
的奇偶性
(2)试判断函数
在
上的单调性,并用函数单调性的定义证明;
(3)若对于任意
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad24741d5bac179c39dbaea856f70f37.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad24741d5bac179c39dbaea856f70f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2472ebf6ae6dcd50d561ee18ecaaa1e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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【推荐3】已知函数
.
(1)解不等式
;
(2)若函数
,其中
为奇函数,
为偶函数,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3633d403f0ac293f3b2599725682c372.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8d99b6df726ac69fae5444e75bc3ba.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc50f609440a36953561a88e8acfee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667ce8df497ebbe542d4cd0d10218530.png)
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解题方法
【推荐1】已知函数
为奇函数.
(1)求实数
的值;
(2)证明函数
在
上的单调递增;
(3)若存在
使得函数
在区间
上的值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137a02b41f72b5ac88b068f1b4324390.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b18edc6e2cea33c80b980949ed7d54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31e72421c0d65e00edb2acce12abffd.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
【推荐2】已知定义域为
的函数
是奇函数.
(1)求
的值;
(2)判断函数
的单调性,并说明理由;
(3)若对于任意
,不等式
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb4c73b4c3335ea930a934722048ece.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995ec593baa4ef50b6d87c78380953d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598f47ddb8a2a3d92d600e53abfbb43e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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