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`        What is a function?`
7 years ago

419 Points
```										Dear Rubankumar
Function can be easily defined with  the help of the concept of mapping. Let X and Y be any two non-empty  sets. "A function from X to Y is a rule or correspondence that assigns  to each element of set X, one and only one element of set Y". Let the  correspondence be 'f' then mathematically we write f:X → Y
where
y = f(x), x ε X and y ε Y. We say that 'y' is the image of 'x' under 'f' (or x is the pre image of y).
Two things should always be kept in mind:
(i)     A mapping f: X → Y is said to  be a function if each element in the set X has its image in set Y. It  is possible that a few elements in the set Y are present which are not  the images of any element in set X.
(ii)    Every element in set X should  have one and only one image. That means it is impossible to have more  than one image for a specific element in set X. Functions can't be  multi-valued (A mapping that is multi-valued is called a relation from X  to Y)

Set 'X' is called the domain of the function 'f'.
Set 'Y' is called the co-domain of the function 'f'.
Set of images of different elements  of set X is called the range of the function 'f'. It is obvious that  range could be a subset of co-domain as we may have few elements in  co-domain which are not the images of any element of the set X (of  course these elements of co-domain will not be included in the range).  Range is also called domain of variation.

The set of values for which a  function is defined is called the domain of the function. The range of  the function is the set of all images of domain of f. In above example,  the set A is the domain of the function f. B is not range but the  co-domain of the function. The range is the subset of the co-domain.
All the best.
AKASH GOYAL

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7 years ago
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