1 . 设f:A→B是集合A到集合B的映射,其中A={实数},B=R,f:x→x2-2x-1,求A中元素1+
的像和B中元素-1的原像.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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12-13高一下·江苏淮安·期末
2 . 已知(x,y)在映射f下的象是(x+y,x2-y),其中x≥0,
求:(2,-2)的原象.
求:(2,-2)的原象.
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11-12高二下·河北衡水·阶段练习
3 . 设f是从集合
到
的映射:
(1)不同的映射f有多少个;
(2)若
,
(3)如果N中的每一个元素在M中都有原象,则这样的映射f有多少个?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7426885ea0a35d7652a90e19b8d2f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533488ef2963c0252508d0ecb32f092d.png)
(1)不同的映射f有多少个;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e053ba0a7ca531fd84ab36a33a64791c.png)
(3)如果N中的每一个元素在M中都有原象,则这样的映射f有多少个?
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4 . 已知向量
,
,
满足
=0,且|
|=|
|,
>0
(1)求向量
;
(2)若映射![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec496800642b689bab8faaf367b5d7.png)
①求映射f下(1,2)原象;
②若将(x,y)作点的坐标,问是否存在直线l使得直线l上任一点在映射f的作用下,仍在直线上,若存在求出l的方程,若不存在说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7506e170ed67615aa7710980a00ca15f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d80f49eb030c398bba929ee599276b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e687ec8f6c55f9a49af42c05c31538.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e273de83d7f518df456d6f6f568ad4e4.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
(2)若映射
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec496800642b689bab8faaf367b5d7.png)
①求映射f下(1,2)原象;
②若将(x,y)作点的坐标,问是否存在直线l使得直线l上任一点在映射f的作用下,仍在直线上,若存在求出l的方程,若不存在说明理由.
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2010·北京海淀·二模
名校
5 . 给定集合
,映射
满足:
①当
时,
;
②任取
若
,则有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
.
.则称映射
:
是一个“优映射”.例如:用表1表示的映射
:
是一个“优映射”.
表1 表2
(1)已知表2表示的映射
:
是一个优映射,请把表2补充完整(只需填出一个满足条件的映射);
(2)若映射
:
是“优映射”,且方程
的解恰有6个,则这样的“优映射”的个数是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe05c3181726d202d021050807378989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92185b667af21e649c9b071042d29af0.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7873a6c263a103ce7a7b1410222bd245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2c865ebac120a4d1e17838ac9dc0ed.png)
②任取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea0eb2f420c6146a0809f01cb3168f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1cd15d46d4fc519ea93da0a7a82a01.png)
.则称映射
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c3373a475f821448143d482d7c0a35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea9eeefda7a3bfe23534700357fbacc.png)
表1 表2
![]() | 1 | 2 | 3 | |
![]() | 2 | 3 | 1 | |
![]() | 1 | 2 | 3 | 4 |
![]() | 3 |
(1)已知表2表示的映射
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe7704aeb096266ab863326b66111d4.png)
(2)若映射
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf5648713989066021d4f7cd433727b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987c640c84d230463ead6415c4c06a72.png)
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