名校
解题方法
1 . 已知定义在
上的函数
满足
,
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6d2a0bceea4d332cbff537430c5848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a87d0288bb21fbffcb60d2bf6695a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc4a027a16191a0ef6a5267a4fcff7e.png)
A.函数![]() | B.![]() |
C.![]() ![]() | D.![]() |
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名校
2 . 已知函数
,则下列有关该函数叙述正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beae01e9e98359fce02acff8a55902da.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |
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解题方法
3 . 函数
是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d532b8d4c5def4e646d8415839b6b4.png)
A.最小正周期为![]() | B.最小正周期为![]() |
C.最小正周期为![]() | D.最小正周期为![]() |
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名校
解题方法
4 . 已知函数
,
满足以下条件:
①
,
;
②
,
,
,
.
(1)求
,
的值.
(2)判断函数
,
的奇偶性,并说明理由.
(3)若
,
,试判断函数
的周期性,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306984f0895ba32a7b3bb607065b1eaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83e9f562c10762097469dea27c1e109.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50ac027c6ebce491ae836524d89901c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ebeb1c1f2826da8a2e0761f2d2ba87d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98eb23b8c96a34dd720e00669aa8ed2b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a078165d75cfb890141845324a6173b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60cf12a81b11e33356fe7e1c9e3d0b9.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfaff6cfe1d15bd64c1fa76af5e52831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158fbbd2cbedeb9a6fa1a900630369f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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名校
5 . 写出一个同时满足下列三个条件的函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81b823d0f2cf80f1aee1ff5a6f6a120.png)
______ .
①
,
;②
,
恒成立.③函数
为偶函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81b823d0f2cf80f1aee1ff5a6f6a120.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e298fe246eef819dd9b1edabe3bb9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e06bd072d0e7b6896d36b1c59ba797b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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6 . 下列函数中,在其定义域内既为奇函数又为增函数的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
7 . 下列函数中是偶函数,且在
上单调递减的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172f1df5c0e107cd16ea0fc22d528258.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
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名校
9 . 已知函数
在定义域
上为偶函数,并且函数
.
(1)判断
的奇偶性,并证明你的结论;
(2)设
,若对任意的
,总存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152043781d916de477d7611cb683a67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c379c978805211415624917ef4c2c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494ca37214184b7f655c7810851d3b72.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8336841b5bc3cb4913835080b9d85933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f9d255ca420fa2486b11fcb7763b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204e6006eacca1a448fe6991f3c121f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bc85e19745af6992cbb72c3fd79ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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名校
解题方法
10 . 定义域为
的函数
,对任意
,且
不恒为0,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937caaff17738b519902a2f3c77b7bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() | B.![]() |
C.![]() | D.若![]() ![]() |
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