解题方法
1 . 已知
是奇函数,且在
内是减函数,又
,则
的解集是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196be101149acfb6a6c4ceca7fc96828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86213096e8b50debedaa87181d7085cc.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2 . 已知函数
,如果关于
的方程
恰有6个不同的实数根,则下列说法一定正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d5529c4cd422853d5f7244414c7d8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a877ab9d6a59eca86bf22e811553928c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 已知
,则在下列区间中,
有实数解的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e9d878a6e7f819f884bacc6731f561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 在
这四个函数中,当
时,使
恒成立的函数的个数是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4beff09ffe9f8b635bb0b6d4f347cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5d446b3dccbaece77ce7308ee8fb0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57efa20c90b7962f9444e7666a12288.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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5 . 如图,
是正方形
的内接三角形,若
,则点
分线段
所成的比为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c922cbd707131b52757c464804ca24f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33c81f03b71c2e436078e43134a247a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/10/5f1feaae-e5b6-4f03-b876-dcc6821fb277.png?resizew=144)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 如图,在
中,
,点
是
上一点,且满足:
,以点
为圆心,
的长为半径作圆交
于点
,交
于点
.若
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4d79b487aa554c647f9b8d9a1a5398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0463b49e10735d11b8b5f550b34186c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979ed6cdbef5a599d780c9989e44f1d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba31188489c03e7aa49d68deb414bcf.png)
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7 . 某市A、B两地之间相距60千米,如图所示,有一条直线铁路经过
地,测量得
地距离铁路48千米.现要在A、B两地之间运送货物,计划从铁路沿线上的
处修筑一条直线公路通往
地,已知公路的运费是铁路运费的2倍,铁路运费为每千米100元,问
点选在何处时可使总运费最少,最少是多少元?
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
8 . 对于函数
下列说法正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abdd99a075638b654d61acfd01130a7.png)
A.![]() ![]() |
B.当且仅当![]() ![]() ![]() |
C.![]() ![]() |
D.当且仅当![]() ![]() |
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9 . 已知定义在
上的函数
的图象关于直线
对称,当
时,
.
(1)求
的值;
(2)求
的函数表达式;
(3)如果关于
的方程
有解,记
为方程所有解的和,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067ed927622208c5e1e33564fb98d4ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e1c64c42b7f3b7fdc396d4756cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15f4b5d828cf068e7044db72c504428.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4627f1cfc3e5d86405dbb6dacfdf95.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)如果关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a675b062ab139d92504d1b9d8667f12e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a675b062ab139d92504d1b9d8667f12e.png)
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10 . 二次函数
为实数,对任意的
都有
和
恒成立.已知
的函数图象与
的图象有且只有一个公共点,这个公共点在第二象限.
(1)求证:
;
(2)若
的最小值为-10,求函数
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047b643568a5f86e592fc2f919cce0f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b273ec7bc43fbbd941d1817a3b841a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c12d98e7a7fef3b4100f52b6125f69b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e9e27ed3ef92663617c2f2815e7025.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a302d9c6416963c881b884bf4e4d783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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