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

The function can be written as:

$\begin{array}{l}y=f(x)\\ or\\ f:x\mapsto f(x)\end{array}$
- For $y=f(x)$ , we say y is a function of x.
- f(x) is also called the value of the function f at x.
- f(x) is read as "f of x".

**Example**:

Given the function $f:x\mapsto 5x+1$ , find the value of

a. $f(2)$

b. $f(-3)$

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

**Answer**:

(a)

$\begin{array}{l}f(x)=5x+1\\ f(2)=5(2)+1=11\end{array}$

(b)

$\begin{array}{l}f(x)=5x+1\\ f(-3)=5(-3)+1=-14\end{array}$

(c)

$\begin{array}{l}f(x)=5x+1\\ f(\frac{2}{5})=5(\frac{2}{5})+1=3\end{array}$