1 . 设函数
的反函数为
,若存在函数
使得对函数
定义域内的任意
都有
,则称函数
为函数
的“Inverse”函数.
(1)判断下列哪个函数是函数
的“Inverse”函数并说明理由.
①
;②
;
(2)设函数
存在反函数
,证明函数
存在唯一的“Inverse”函数的充要条件是函数
的值域为
;
(3)设函数
存在反函数
,函数
为
的一个“Inverse”函数,记
,其中
,若对函数
定义域内的任意
都有
,求所有满足条件的函数
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a2a1822ac7392b61b2c0fffc1fbc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346b6e84aa00abca0241eb18b6a5e38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)判断下列哪个函数是函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45afdf4d717bb03adac6b899c367acb.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0febd73692b5a2d8b559c2b4bb67ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8904fa3def3f943c3d2ab20dbc632e.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a2a1822ac7392b61b2c0fffc1fbc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12042034d9bc24cc31f15895dce44b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a2a1822ac7392b61b2c0fffc1fbc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641067daedeade49b5d9924c6e245cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39e176af5b23719580d925e792aa8b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee724824f6623445bf571d1fffc5c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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