Notation of Function


As shown in figure above, for a function f : X Y , each element x in the domain X has a unique image y in the codomain Y. 

The function can be written as:
y = f ( x ) o r f : x f ( x )
  1. For y = f ( x ) , we say y is a function of x.
  2. f(x) is also called the value of the function f at x.
  3. f(x) is read as "f of x".

Example:
Given the function f : x 5 x + 1 , find the value of
a. f ( 2 )
b. f ( 3 )
c. f ( 2 5 )

Answer:
(a)
f ( x ) = 5 x + 1 f ( 2 ) = 5 ( 2 ) + 1 = 11 (b)
f ( x ) = 5 x + 1 f ( 3 ) = 5 ( 3 ) + 1 = 14 (c)
f ( x ) = 5 x + 1 f ( 2 5 ) = 5 ( 2 5 ) + 1 = 3

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