Question

高一数学题：下列对应中是从集合A到集合B的映射的为

1.A={矩形},B={实数},f为求矩形的面积
2.A={平面α内的圆}，B={平面α内的矩形}，f为作圆的内接矩形
3.A=R，B={x∈R|x>0}，f:x→y=x²+1
4.A=R,B=R,f：x→y=1/x
5.A={x∈R|1<=x<=2},B=R,f：x→y=2x+1
打字真心累啊，但我真的想弄懂这道题，请高手给出详解。谢谢！

Answer 1

答案：1，3，5
映射的定义：如果存在一个对应f，使得对A中的每个元素a，按对应f，在B中有唯一确定的元素b与之对应，则称f为从A到B的映射，记作f：A→B。

简单说说A的集合是定义域，通过对应f（一般就是函数），会得到一一对应的另一个集合，就是值域，如果该集合包含于集合B就说明对应f是从集合A到集合B的映射，
1，矩形的面积是一个正实数，包含于实数集合，正确
2，平面圆内接矩形对应多个，错误
3，对应f后值域为x≧1，包含于集合x>0，且一一对应，正确
4，x=0时在B集合找不到对应的映射，错误
5，对应f后值域为[3,5]包含于集合B，且是一一对应关系，正确

Answer 2

解：
1.矩形面积大于0，每个矩形都有确定的面积，A中的元素映射后都能在B中找到唯一对应元素，A→B的映射成立。

2.平面内任一圆有无数内接矩形，A中的元素映射后能在B中找到不唯一对应元素，A→B映射不成立。

3.对R中的x，x²+1≥1＞0，y值唯一且都在>0的范围，A中的元素映射后都能在B中找到唯一对应元素，A→B映射成立。

4.对R中的0，y=1/x没有意义，A中的元素0映射后不能在B中找到唯一对应元素，A→B映射不成立。

5.对1≤x≤2的任意x，2x+1唯一且存在于R中，A中的元素映射后都能在B中找到唯一对应元素，A→B映射成立。

综上，1.3.5.是A→B的映射，2.4.不是A→B的映射。（楼上都错了）

希望能帮到你！

Answer 3

设A、B是两个非空集合，如果存在一个法则f，使得对A中的每个元素a，按法则f，在B中有唯一确定的元素b与之对应，则称f为从A到B的映射，记作f：A→B。

其中，b称为元素a在映射f下的像，记作：b=f(a); a称为b关于映射f的原像。集合A中所有元素的像的集合记作f(A)。
映射，或者射影，在数学及相关的领域还用于定义函数。函数是从非空数集到非空数集的映射，而且只能是一对一映射或多对一映射。

1.是。对任意矩形，求其面积，值都可以在B找到，确定且唯一。
2.不是。平面a内可与A对应矩形不唯一。
3.是。
4.不是。当x=0时，f无意义。不存在B中相应元素与之对应。
5.是。

Answer 4

1是，因为每个矩形的面积是唯一的。
2否，因为一个圆能作出任意个内接矩形。
3是，a中元素平方再加一即可。
4是，a中元素取自身即可。
5是。

Answer 5

好久没做映射的题都忘了，5题,3-5

Answer 6

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