1.2.1 Notation of Function

As shown in figure above, for a function

f : 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) \\ o r \\ f : x \mapsto f (x) \end{array}

Example:
Given the function

f : x \mapsto 5 x + 1

, find the value of
a.

f (2)

f (- 3)

f (\frac{2}{5})

Answer:
(a)

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

(b)

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

(c)

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