Notation of Function


As shown in figure above, for a function \(f:{\rm{ X}} \to Y\), each element x in the domain X has a unique image y in the codomain Y. 

The function can be written as:
\[\begin{array}{l} y = f(x)\\ or\\ f{\rm{ }}:x \mapsto f(x) \end{array}\]
  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 \(f{\rm{ }}:x \mapsto 5x + 1\) , find the value of
a. \(f(2)\)
b. \(f( - 3)\)
c. \(f(\frac{2}{5})\)

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