# 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. $$f(\frac{2}{5})$$

$f(x)=5x+1 f(2)=5(2)+1=11$ (b)
$f(x)=5x+1 f(−3)=5(−3)+1=−14$ (c)
$f(x)=5x+1 f( 2 5 )=5( 2 5 )+1=3$