解题方法
1 . 定义域为R的函数
的图象关于点
对称,函数
的图象关于直线
对称.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ec894c353fcfc8a19e9ac4db5b3eb6.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de0329cd0d5164adbdaf97d0f5f758a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7d4b04fdae421a5ad24c5fee042983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104375baf5cef5eb92cfc7cf13b80193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ec894c353fcfc8a19e9ac4db5b3eb6.png)
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2 . 已知函数
有两个零点
,
,则可设
,由
可知
,
,这就是一元二次方程根与系数的关系,也称韦达定理.多项式运算可以更好地理解“韦达定理”,类似地,若
为方程
的3个实数根,设
,则
为
的系数,
为
的系数,
为常数项,于是有
,
,
实际上任意实系数
次方程都有类似结论.设方程
的四个实数根为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade331851befdd556917c4a9de446a38.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8617d09dc5c1fe2639ac969370a572.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bd0587f5d6a3b5db9e4a93e0dbc0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b5ee46e4c079505266ef307a783c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cce519ecad53af16de6b8fa9434110e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05dd02b6f561dcf94bab8a3160108d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897630dd340ec6c6b20cdd754d0a12c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db92d5c0ce7887591208ecefbf2c557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e94cb8a9c68817f1cfb36703e34165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704bf1ed4962891486b3e577f411d76b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55a81cc6b05568ff6a73fec5060d83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002631ce8fcc3b3fff84adf8eaca728e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42879b831382d3d84c43a70a3ed78f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1d0b683ce81f1619626dcdca6b5a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c100d28933d6637f946f31bb93c42418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b60fd3ebd3200f078155fbeeb44fc51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade331851befdd556917c4a9de446a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8617d09dc5c1fe2639ac969370a572.png)
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解题方法
3 . 设函数
是定义在R上的奇函数,对任意
,都有
,且当
时,
,若函数
(
且
)在
上恰有4个不同的零点,则实数a的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dafce249be1aeee0581417db4ce841db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ea832b11f5a84b9bf3020271480631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900b106c2b44b211c60b0ba9c2cf6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0b226b2da37b802313e88a4cd8f987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77b96fc51eb8a9d03ced254ce8b78be.png)
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解题方法
4 . 已知
是幂函数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5c145746b575278538f9befc802d9b.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca20cc355e56e3a48624bb780981ef0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5c145746b575278538f9befc802d9b.png)
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解题方法
5 . 已知幂函数
为奇函数.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9433baccaba757ce3b6c041f817b1b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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6 . 已知函数
在
上是增函数,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5c7bc3df3b3557876bfd340f734a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189b2da6c420bf8f8900002d14f65f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 科学家研究发现,地震时释放出的能量
(单位:焦耳)与地震里氏震级
之间的关系为
,里氏9.0级地震释放的能量是7.0级地震所释放能量的______ 倍.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f81e0e9e0749ac2e043ac323ee40bf.png)
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8 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d04d73c5b02fc71dabeec66648fc1601.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfefbb622a4f78576744d555e6c08dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d04d73c5b02fc71dabeec66648fc1601.png)
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9 . 已知
是定义在
上的增函数,且
的图象关于点
对称,则关于
的不等式
的解集为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e99bebf8db0d314aacb2cb1f09bf48c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6404d8a4da60c5670e9b4798d8b1d9.png)
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解题方法
10 . 函数
的定义域为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2022f128fdee960d0a9bbc928813bf.png)
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