Now, in functions or mapping we will study about special type of relations called functions or mapping. To understand them, let us take few real life examples.
| All these questions have
unique answers. Let us
see how we can relate
this in learning mapping.
● From where does the sun rise?
● Which is the capital of India?
● What is the successor of 4?
● What is the sum o f 5 and 3?
If A and B are two non-empty sets, then a relation ‘f‘ from set A to set B is said to be a function or mapping,
● If every element of set A is associated with unique element of set B.
● The function ‘f’ from A to B is denoted by f : A → B.
● If f is a function from A to B and x ∈ A, then f(x) ∈ B where f(x) is called the image of x under f and x is called the pre image of f(x) under ‘f’.
For f to be a mapping from A to B:
● Every element of A must have image in B. Adjoining figure does not represent a mapping since the element d in set A is not associated with any element of set B.
● No element of A must have more than one image. Adjoining figure does not represent a mapping since element b in set A is associated with two elements d, f of set B.
● Different elements of A can have the same image in B. Adjoining figure represents a mapping.
Every mapping is a relation but every relation may not be a mapping.
Let us recall and review the function as a special kind of relation suppose, A and B are two non-empty sets, then a rule 'f' that associates each element of A with a unique element of B is called a function or a mapping from A to B.
If 'f' is a mapping from A to B,
we express it as f: A → B
we read it as 'f' is a function from A to B.
If ‘f ' is a function from A to B and x∈A and y∈B, then we say that y is the image of element x under the function ' f ' and denoted it by f(x).
Therefore, we write it as y = f(x)
Here, element x is called the pre-image of y.
Thus, for a function from A to B.
● A and B should be non-empty.
● Each element of A should have image in B.
● No element of 'A' should have more than one image in 'B’.
● Two or more elements of A may have the same image in B.
● f : x → y means that under the function of 'f' from A to B, an element x of A has image y in B.
● It is necessary that every f image is in B but there may be some elements in B which are not f images of any element of A.
● Relations and Mapping
● Relations and Mapping - Worksheets