# 1.3 Composite Function

### Composite Function

If function $f:X↦Y$ ,
and function $g:Y↦Z$ ,
hence, composite function $gf:X↦Z$

Example:
If, $f:x↦2x+5$ and $g:x↦{x}^{2}-1$ , find $gf\left(2\right)$

$\begin{array}{l}f\left(x\right)=2x+5\\ f\left(2\right)=2\left(2\right)+5=9\end{array}$
$gf\left(2\right)=g\left[f\left(2\right)\right]=g\left(9\right)$
$\begin{array}{l}g\left(x\right)={x}^{2}-1\\ gf\left(2\right)=g\left(9\right)={9}^{2}-1=80\end{array}$