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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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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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3 . 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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4 . 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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5 . 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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6 . 已知函数
满足
,且
.
(1)求
的解析式,并判断
的奇偶性;
(2)若对任意
,
,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655edc93542cc9c0a3bad2bc4ac66b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926634d86f899dab37e01f0a7e4bd511.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fc4b242b118b3ba3a246d337cdc834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a655cd454807e618127ffb1e3c34d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5981abaf2c2b80a8b8dfc54edb12fa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172f1df5c0e107cd16ea0fc22d528258.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
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8 . 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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9 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8f6b907e5e8c04d885e3c98b32c615.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() |
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10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8460bfd4440ead8dd7d8a5287b84f0.png)
(1)判断函数
的奇偶性;
(2)证明:函数
在区间
上单调递增;
(3)令
(其中
),求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8460bfd4440ead8dd7d8a5287b84f0.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe7bcabcfb85b89d906401bb4a64c6b.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd39a020accc12c2a2d1540207face6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8a07f439f530a67ec0ff4fbbdd9695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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