定义函数
:对于任意实数
,如果存在整数
满足
,那么
,设函数
,以下命题:
①函数
是奇函数;
②函数
的值域为
;
③方程
有无数解:
④函数
的最小正周期为
;
⑤函数
不存在单调递减区间.
其中真命题是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a61c12cee2651c4b38806bf1e1fe03c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91090c0f13052f9c91ad0546ce422e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb1b36d711ea3af8b6f04101c6c2255.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
③方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb381ac86308c6249bc7e8737cdc668d.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
⑤函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
其中真命题是
更新时间:2020-02-11 00:09:34
|
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解题方法
【推荐1】已知定义在
上的函数
对任意实数
满足
,
,且
时,
,则函数
与
的图象的交点个数为______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
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【推荐2】阅读下列材料,回答所提问题:设函数
,①
的定义域为
,其图像是一条连续不断的曲线;②
是偶函数;③
在
上不是单调函数;④
恰有
个零点,写出符合上述①②④条件的一个函数的解析式是______ ;写出符合上述所有条件的一个函数的解析式是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
【推荐3】已知函数
,则使不等式
成立的实数
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ad38d56265670143770dea678188fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e2200e2760bc1bffecb37ae2b8a87b.png)
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【推荐1】已知
是定义在
上的奇函数,且
的图象关于直线
对称,当
时,
,则使得
成立的区间是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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【推荐2】已知函数
,若
互不相等),且
的取值范围为
,则实数
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f36aa67344fba85fd10ee5862ae2483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a706f568250af60bb0767d0fd37e98.png)
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【推荐1】对于函数
,若在定义域存在实数
,满足
,则称
为“局部奇函数”.若函数
是定义在
上的“局部奇函数”,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐2】设函数
的定义域为
,如果对于任意的
,存在唯一的
,使
为常数),则称函数
在
上均值为
.下列五个函数:①
;②
;③
;④
;⑤
.则满足在其定义域上均值为2的所有函数的序号是___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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