1.3 Composite Function - SPM Additional Mathematics

Composite Function

If function

f : X \mapsto Y

$f : X \mapsto Y$ ,
and function

g : Y \mapsto Z

$g : Y \mapsto Z$ ,
hence, composite function

g f : X \mapsto Z

$g f : X \mapsto Z$

Example:
If,

f : x \mapsto 2 x + 5

$f : x \mapsto 2 x + 5$ and

g : x \mapsto x^{2} - 1

$g : x \mapsto x^{2} - 1$ , find

g f (2)

$g f (2)$

Answer:
$\begin{array}{l} f (x) = 2 x + 5 \\ f (2) = 2 (2) + 5 = 9 \end{array}$ $\begin{array}{l} f (x) = 2 x + 5 \\ f (2) = 2 (2) + 5 = 9 \end{array}$

$g f (2) = g [f (2)] = g (9)$ $g f (2) = g [f (2)] = g (9)$

$\begin{array}{l} g (x) = x^{2} - 1 \\ g f (2) = g (9) = 9^{2} - 1 = 80 \end{array}$ $\begin{array}{l} g (x) = x^{2} - 1 \\ g f (2) = g (9) = 9^{2} - 1 = 80 \end{array}$

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Composite Function

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