解题方法
1 . 我们知道
与
(
且
)互为反函数,它们具有以下性质:①图象关于直线
对称;②
的定义域是
的值域,
的值域是
的定义域,反之亦然;③若点
在函数
的图象上,则点
一定在函数
的图象上.
(1)若函数
与
互为反函数,求实数a,b的值;
(2)运用(1)题中得到的函数
,若对
,使得
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.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/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493d16a261e909d2faf6b5386b8fa5d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab3a3d264dba79d3e2995bec4ad3ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1a3f631ea291a932f4bc466556a2c1.png)
(2)运用(1)题中得到的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0ed188d083966baaae94e6b86064f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976472fb4679ad2d8ec2f928f684650b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d25a5b1e41c9fa76ece3b27d81b0e8f.png)
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解题方法
2 . 如图所示,若将边长为
的正方形纸片
折叠,使得点
始终落在边
.(不与点
重合),记为点
,点
折叠以后对应的点记为点
为折痕.设点
和点
间的距离为
,折痕
的长度为
,四边形
的面积为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b1fe1b971b780e443a9b13621611c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243cdaf33d01bbb6bc3c9c514c00285f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3160fce05b551569b8c7b5de6dd8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea810d57d5f7e069b202d5dff4f35283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bedde879f99aed69d745d5ec8fe62084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8f9c4048d29b6c50b5a750f3d35b99.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/033819c4-a699-4bbb-8d87-6ce6e5f3a42e.png?resizew=174)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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