1.3a Composite Function

Posted on April 18, 2020 by user

Composite Function

If function

f : X \mapsto Y

,
and function

g : Y \mapsto Z

,
hence, composite function

g f : X \mapsto Z

Example:
If,

f : x \mapsto 2 x + 5

and

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

, find

g f (2)

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

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

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

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