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Functions or Mapping
● From where does the sun rise? Mapping or Functions:If A and B are two nonempty 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’. Note: ● 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.
Function as a special kind of relation:Let us recall and review the function as a special kind of relation suppose, A and B are two nonempty 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 preimage of y. Thus, for a function from A to B. ● A and B should be nonempty. ● Each element of A should have image in B. ● No element of 'A' should have more than one image in 'B’. Note: ● 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. Related Concepts ● Ordered Pair ● Cartesian Product of Two Sets ● Relation ● Domain and Range of a Relation ● Domain Codomain and Range of Function 7th Grade Math Problems



