RELATIONS AND FUNCTIONS · Part 16

Example Let f = {( , ), ( , ), ( , – ), (– , – )} be a linear function from Z into Z . Find f ( x ). Solution Since f is a linear function, f ( x) = mx + c. Also, since ( , ), ( , – ) ∈ R, f ( ) = m + c = and f ( ) = c = – . This gives m = and f ( x ) = x – . Example Find the domain of the function f x Solution Since x – x + = ( x – ) ( x – ), the function f is defined for all real numbers except at x = and x = . Hence the domain of f is R – { , }. Example The function f is defined by f ( x ) = x, x , x , x <    + >  Draw the graph of f ( x ). Solution Here, f ( x ) = – x , x < , this gives f (– ) = – (– )= ; f (– ) = – (– ) = , f (– ) = – (– )= f (– ) = – (– ) = ; etc, and f ( ) = , f ( ) = , f ( ) = f ( ) = and so on for f ( x ) = x + , x > . Thus, the graph of f is as shown in Fig . Fig . MATHEMATICS Miscellaneous Exercise on Chapter . The relation f is defined by ( ) = x , f x x,  ≤≤  ≤≤  The relation g is defined by , , g x  ≤ ≤  = ≤ ≤  Show that f is a function and g is not a function. . If f ( x ) = x , find ( ) ( ) ( ) f –