Module 1 : Real Numbers, Functions and Sequences
Lecture 1 : Real Numbers, Functions    [ Section 1.2 : Functions ]
 
(iv)

 If is one -one, the function  , defined byfor , is called the inverse function.
(v)
 We say   is onto (or surjective ) if.
(vi)
 A function   is called bijective if it is injective as well as surjective.
(vii)

 If   and  with ,  then the composite function is the function go  defined by  for .
1.2.4   Note:
  For , saying that a function , is onto means that the horizontal line at every point  meets the graph of the function at least once. Similarly, saying that the function is one -one means that the horizontal line at every point  meets the graph of the function at most once.    
   
  Click here to see an interactive visualization:  Applet 1.1
   
  Click here to see an interactive visualization:  Applet 1.2
1.2.5   Absolute Value function :
   
  The function  :   defined by
                       
is called the absolute value function and  | |  is called the absolute value of  .
1.2.6   Theorem :
  For every  the following results are true:
(i)  if  and only if , ( that is,  ,  and conversely ).
(ii) .
(iii)
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