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CBSE Class 12 – Maths, Physics, Biology, Chemisrty,Commerce, Computer
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Few concepts in detail
(Note: To understand the concept clearly, watch our respective 3D animated videos while reading this article, as the illustrations are based on this.)
function
Goal:
In this session we will understand the concept of function. We drew dots on graph paper. The points are given by their coordinates. (4, 5), (5, 4), (3,5, 4) etc.
We know that the first number gives us the xcoordinate, that is, the distance from the origin along the xi axis, the second number gives us the ycoordinate, that is, the distance from the origin to along the y axis. It is for this reason that if we change the order of the numbers, we get a different point. (4, 5) and (5, 4) are two different points. This arrangement of pairs of numbers where the order must be maintained is called an ordered pair.
The cross product of two sets, AxB = (a, b) I ae A and be B To explore all the possibilities, let’s have two sets. Seven A with five robots and seven B with seven bikes.
Now let’s match a robot with the bike that matches its color.
Case I:Green robot with green bike. Blue robot with blue bike etc. In this box we find that each robot has only one bike for itself.
Case 2: Let the orange bike be replaced by a light green one.
Now we find that the robot with orange color does not have a bike for itself.
Case 3: Take the light green and purple bikes and replace them with orange bikes. Matching sets again.
Now we find that the orange robot has two bikes for himself. Thus we observe that in the first case each robot in set A has a bicycle for itself, and there are 2 spare bicycles. In the second case there is a robot without a matching bike and finally in the third case we have a robot that has more than one matching bike. These conditions lead us to the definition of a function.
A function is a subset of the cross product of two nonempty sets A and B such that every element of set A has a unique image in set B.
The function is represented by lowercase letters, for example, Function f:A>B. Set A is called domain and set B is domain Co. This further implies that no element of A can have more than one image in B. And further, there should be no element of A that does not have an image in B. Mathematically it implies that no two pairs ordered that will have the same first element. .
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