Function as a Correspondence
Function as a correspondence
Let A and B be two non-empty sets. Then a function ‘f ‘ from set A to set B is a rule or method or correspondence which associates elements of set A to elements of set B such that:
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| Fig. 2(a) |
(i) all elements of set A are associated to elements in set B.
(ii) an element of set A is associated to a unique element in set B.
In other words, a function ‘f ‘ from a set A to a set B associates each element of set A to a unique element of set B.
Terms such as “map” (or “mapping”), “correspondence” are used as synonyms for “function”. If f is a function from a set A to a set B, then we write f : A → B which is read as f is a function from A to B or f maps A to B.
If an element a new a ∈ A is associated to an element b ∈ B, then b is called “the f-image of a” or “image of a under f ” or “the value of the function f at a “. Also, a is called the pre-image of b under the function f. We write it as b = f (a).
The set A is known as the domain of f and the set B is known as the co-domain of f The set of all f -images of elements of A is known as the range of f or image set of A under f and is denoted by f (A).
Thus, f(A) = {f(x) 
∈ A} Range of f.
∈ A} Range of f. A visual representation of a function is shown in Fig. 2(a)
