Functions in R

 

A rule of correspondence   f   is called a real value function if it associates each member   x   of the set   A   to an uniquely determined member    y    (called image of   x ) of   B  , a subset of   R   . is denoted by


          f: A--> B   or    y=f(x) ,


indicating that the real number   y    corresponds to 

                                                x     is element of    A

                                             under the rule      f      .


The set  A  is called domain of the function and

set   f(A)={ y/ y=f(x) ;   x   is element of  A}

i.e. the set of images of  A  is called the range of   f  .

Also   x   is called the independent variable and    y   is called a dependent variable .

Features of a function    y=f(x)   in    R   are as follows ;


1)   y    is uniquely determined for every value of   x   from the domain . The value of    y   corresponding to the value    a    of    x    is denoted by     f(a)  .


2)   For two or more values of    x ,   y    can have the same value .


3)   The image i.e. the value of   y    for a prescribed value of    x    is obtained by substituting the value of    x    in the equation connecting    x , y    to describe the rule    f    .