CBSE CLASS 12
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Few concepts in detail
(Note: To clearly understand the concept, watch our respective 3D animated videos while reading this article as the illustrations are based on them.)
function
objective:
In this session we will understand the concept of a function. We drew dots on a 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, ie the distance from the origin along the xaxis, and the second number gives us the ycoordinate, ie the distance from the origin along the yaxis. Because of this, if we change the order of the numbers, we get a different point. (4, 5) and (5, 4) are two different points. Such an arrangement of pairs of numbers, where the order should be preserved, is called an ordered pair.
The cross product of two sets, AxB = {(a, b) I ae A and be B} To explore all possibilities, we have two sets. Set A with five robots and Set B with seven bikes.
Now let’s pair a robot with the bike that matches its color.
Case I: Green robot with green bike. Blue robot with blue bike etc. inside case We note that each robot has only one bike of its own.
case 2: Have the orange bike replaced with a light green bike.
Now we notice that the robot with orange color does not have a bike of its own.
case 3: Take the light green and purple bikes and replace them with orange bikes. Put the sentences back together.
Now we notice that the orange robot has two bikes of its own. So we find that in the first case, each robot from set A has a bike for itself and there are 2 spare bikes. In the second case we have a robot with no 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 each element of set A has a unique image in set B.
The function is represented by lowercase letters, e.g. B. Function f:A>B. Set A is called domain and set B is called codomain. This further implies that no element of A can have more than one image in B. And there shouldn’t be any element of A that doesn’t have an image in B either. Mathematically, this implies that no two ordered pairs will have the same first element.
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 CBSE class 12
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