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Rubankumar S Grade: 10
        What is a function?
7 years ago

Answers : (1)

AKASH GOYAL AskiitiansExpert-IITD
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


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.




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7 years ago
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