A rule or principle or fundamental condition which tells a relationship between two sets’ elements is defined function.
Consider X and Y are two different sets which contain different elements. The elements of X and Y sets are given below.
X = {a, b, c, d}
Y = {A, B, C, D}
As per our assumption, set X contains four elements a, b, c and d. Similarly, the set Y contains four elements A, B, C and D. However, the elements of two sets are mathematically maintaining a relationship. It can represent in a picture as shown in the image below.
You can clearly understand that the elements of set Y are images of set X. In other words, the corresponding elements of a, b, c and d belong to set X are A, B, C and D respectively which are part of set Y. The image or associated or corresponding value of a is A. Similarly, the corresponding values of b, c and d are B, C and D as per this graphical representation.
However, if a mathematical relationship calls as a function, it should satisfy two major conditions.
- All elements of set X are associated to elements of set Y.
- An element of set X is associated to unique element of set Y.
This graphical representation satisfied the above conditions. So, it is called a function. It is actually represent with an English alphabet f.
This mathematical relationship is written mathematically f: X → Y. It can also be written.
Mathematically, this mathematical relation can be expressed as written below.
Y = F(X)
Let us verify this with our function’s elements. Put X = a and then you get Y = A.
A = F(a)
Similarly,
B = F(b)
C = F(c)
D = F(d)
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