Answer
$\left( \dfrac{f}{g} \right)(5)=-7$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
\left( \dfrac{f}{g} \right)(5)
,$ given
\begin{array}{l}\require{cancel}
f(x)=x^2+3
\\
g(x)=-2x+6
,\end{array}
use the definition of the appropriate function operation. Then substitute $x$ with $
5
.$
$\bf{\text{Solution Details:}}$
Since $\left( \dfrac{f}{g} \right)(x)=\dfrac{f(x)}{g(x)},$ then
\begin{array}{l}\require{cancel}
\left( \dfrac{f}{g} \right)(x)=\dfrac{x^2+3}{-2x+6}
.\end{array}
Substituting $x$ with $
5
,$ then
\begin{array}{l}\require{cancel}
\left( \dfrac{f}{g} \right)(5)=\dfrac{(5)^2+3}{-2(5)+6}
\\\\
\left( \dfrac{f}{g} \right)(5)=\dfrac{25+3}{-10+6}
\\\\
\left( \dfrac{f}{g} \right)(5)=\dfrac{28}{-4}
\\\\
\left( \dfrac{f}{g} \right)(5)=-7
.\end{array}
