1 . 设有两个集合
,如果对任意
,存在唯一的
,满足
,那么称
是一个
的函数.设
是
的函数,
是
的函数,那么
是
的函数,称为
和
的复合,记为
.如果两个
的函数
对任意
,都有
,则称
.
(1)对
,分别求一个
,使得
对全体
恒成立;
(2)设集合
和
的函数
以及
的函数
.
(i)对
,构造
的函数
以及
的函数
,满足
;
(ii)对
,构造
的函数
以及
的函数
,满足
,并且说明如果存在其它的集合
满足存在
的函数
以及
的函数
,满足
,则存在唯一的
的函数
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2317480af8719266bb92ee59d6b2c3b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf13fc6f6469b51cba724df6701f2016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acae4bf2a6bead9d904b70d0480fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f484115a9df1b6060d6b14df85c6f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acae4bf2a6bead9d904b70d0480fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b9b582f8426f1269b54ee910b97f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5609d6ec9ef33f11e359f35d27289623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e50933c5e999ca64d3046fe1fa84dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169ccf0e6e7ada48126feac1e67de0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276509f01529d982ab21e479a4619268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c775f6d86ae37c1d2251ee935f17c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acae4bf2a6bead9d904b70d0480fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674c6027fe6ac3a582bced0c2cde8c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a719e840660f5c08ec081ee661d7ac77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e9af5ad8e107db8512bc54e627d565d.png)
(1)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585be45e95d45f86456790525ef6e24d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136c6a4d3de85560224cc18a46c60231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4e2f595418c82b94ef66a6f526e63d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169ccf0e6e7ada48126feac1e67de0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5609d6ec9ef33f11e359f35d27289623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(i)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2836fa0f9aca03548ec72d1bd49d9ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07005ca97e96fafcef55ec126ba84f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0603e63b4cc9944c237e4a776f0688b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e52c39d6ffd048bfa7bc97d849029ea.png)
(ii)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2836fa0f9aca03548ec72d1bd49d9ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07005ca97e96fafcef55ec126ba84f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0603e63b4cc9944c237e4a776f0688b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e52c39d6ffd048bfa7bc97d849029ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686c919499ba2092f18a1555c5e1bce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a886d45a46bdde67115c5911cb85ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f2e87a902efe698955b1b7d805690b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735dd0765a19f97a03c9db4babb64ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d249478e181957c41657b2c61c1ad50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916a915b809c8d0028cbe245e0149e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3909505a98004589b98f9d14e1bd41d.png)
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