名校
解题方法
1 . 已知函数
,则不等式
的解集为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cd45561a50531a9253bce3bb5a3456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c4f8e29aa79e03637410f04887145b.png)
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2 . 函数
,直线
与函数
的图象相交于四个不同的点,从小到大,交点横坐标依次记为
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92d0e798924d83a5ff96c5fa8a3e0c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35893041a02be39c9d0c1e9b329556eb.png)
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3 . 德国著名数学家狄利克雷在数学领域成就显著,他是数学史上第一位重视概念的人,并且有意识地“以概念代替直觉”,以其名命名的函数
为狄利克雷函数,现定义一个与狄利克雷函数类似的函数
为“
函数”,则关于狄利克雷函数和
函数有以下四个结论:
(1)
;
(2)函数
既是偶函数又是周期函数;
(3)
函数图象上存在四个点
、
、
、
,使得四边形
为矩形;
(4)
函数图象上存在三个点
、
、
,使得
为等边三角形.
其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5219e7db4b2d93eb85630908b9e3c7f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767f9c9e86126257504dd45a2e94260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7298e41399f66a12e2dad0a716106b.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8238fba9b391d01ceb071e78ee221035.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
其中所有正确结论的序号是
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4 . 已知
为定义在
上的偶函数,当
时,有
,且当
时,
.给出下列命题,其中正确的命题的个数为________ .
(1)
;
(2)函数
在定义域上是周期为2的周期函数
(3)直线
与函数
的图像有1个交点;
(4)函数
的值域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275815073d040d04fe4820f9841b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d31d07e0e178dd81de9ab409d9475e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f52f6ee8ead43c46f73102b87a2d943.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efcc52ab5b5bfeb2d37739f49d6cbdae.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(4)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
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解题方法
5 . 已知函数
是定义在
上的周期为2的偶函数,
,
,则函数
的图象与函数
的图象交点个数为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b49e9a0e47989e60ea6873018771d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35af97da89bd866e9a74a6bdc4f3bd06.png)
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解题方法
6 . 已知
是定义域为
的奇函数,且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf7ee48f89034c50f17253321722d3a.png)
__________ .
![](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/0a854227d789fa69c4f13371affb4ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45af87a3c97cf74f6bd13977827315d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf7ee48f89034c50f17253321722d3a.png)
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解题方法
7 . 设函数
,则满足
的
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13440b2327f9a935fd46a818b1920452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77d1e48ce8103f47624ca139683fd27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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8 . 若函数
是
上的单调函数,且对任意实数x,都有
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4138e3a956d50c217cdd4799ff1edd.png)
____________ .
![](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/c49791bb3186afedd8ac7b5163355dca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4138e3a956d50c217cdd4799ff1edd.png)
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解题方法
9 . 若函数
有最小值,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0662960ce3047e33fe7bf2ffd35b5b66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
10 . 已知函数
,则不等式
的解集为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafee19047be9b4bd892102e951fd1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
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