Answer
$\left( \dfrac{f}{g} \right)(0)\text{ is undefined}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the value of the given expression, $
\left( \dfrac{f}{g} \right)(0)
,$ 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)(0)=\dfrac{f(0)}{g(0)}
\text{ (Equation *)}
.\end{array}
Based on the given table, when $x=
0
,$ the value of $f(x)$ is $
5
.$ Hence, $
f(0)=5
.$
Based on the given table, when $x=
0
,$ the value of $g(x)$ is $
0
.$ Hence, $
g(0)=0
.$
By substitution, Equation * becomes
\begin{array}{l}\require{cancel}
\left( \dfrac{f}{g} \right)(0)=\dfrac{f(0)}{g(0)}
\\\\
\left( \dfrac{f}{g} \right)(0)=\dfrac{5}{0}
\\\\
\left( \dfrac{f}{g} \right)(0) \text{ is undefined}
.\end{array}
