Nature of Functions:

I. One – One Function:
            Let 'A' and 'B' be any two non–empty sets then a function '' from A to B is called one–one function, if and only if distinct elements of set A have distinct elements of set B.
            e.g.                   ,
            
In Mathematically,
            Let be a function then '' is called one–one function iff
            (i)
            (ii)
II.   Onto Function:
            Let 'A' and 'B' be any two non–empty sets then a function '' from A to B is called onto function iff
                                   Range of
                e.g.                   ,     
            
                               Range of
III.   Bijective Function:
            A function which is one–one as well as onto function is called bijective function.
            e.g.             ,
            
Periodic Function:
            A function is said to be periodic if there is a positive numbersuch that
                                         
            The smallest such value of  is called the period of
            
            
                                                                                                                                                                                        
                                                                                                                                                                                        
                                                                                                                                                                                           

            

Operations on Functions:
            If '' and '' are the functions of 'x'; then the sum of, difference of  and quotient are defined as.

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(Types of Functions)

Function and Limits

(Concept of Limit)