Answer
$\left( \dfrac{f}{g} \right)(3)=1$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the value of the given expression, $
\left( \dfrac{f}{g} \right)(3)
,$ use the definition of the appropriate function operation. Then substitute the values in the given table.
$\bf{\text{Solution Details:}}$
Using $\left( \dfrac{f}{g} \right)(x)=\dfrac{f(x)}{g(x)},$ then
\begin{array}{l}\require{cancel}
\left( \dfrac{f}{g} \right)(3)=\dfrac{f(3)}{g(3)}
\text{ (Equation *)}
.\end{array}
Based on the given table, when $x=
3
,$ the value of $f(x)$ is $
9
.$ Hence, $
f(3)=9
.$
Based on the given table, when $x=
3
,$ the value of $g(x)$ is $
9
.$ Hence, $
g(3)=9
.$
By substitution, Equation * becomes
\begin{array}{l}\require{cancel}
\left( \dfrac{f}{g} \right)(3)=\dfrac{f(3)}{g(3)}
\\\\
\left( \dfrac{f}{g} \right)(3)=\dfrac{9}{9}
\\\\
\left( \dfrac{f}{g} \right)(3)=1
.\end{array}
