Answer
$\left(\dfrac{f}{g}\right)(-1)\text{ is undefined (does not exist)}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the expression, $
\left(\dfrac{f}{g}\right)(-1)
,$ given that
\begin{array}{l}\require{cancel}
f(x)=3x^2-4 \text{ and }
\\g(x)=x^2-3x-4
,\end{array}
use the definition of the appropriate function operation. Then substitute $x$ with $-1.$
$\bf{\text{Solution Details:}}$
Using $\left(\dfrac{f}{g}\right)(x)=\dfrac{f(x)}{g(x)},$ then
\begin{array}{l}\require{cancel}
\left(\dfrac{f}{g}\right)(x)=\dfrac{3x^2-4}{x^2-3x-4}
.\end{array}
Sustituting $x$ with $-1,$ then
\begin{array}{l}\require{cancel}
\left(\dfrac{f}{g}\right)(-1)=\dfrac{3(-1)^2-4}{(-1)^2-3(-1)-4}
\\\\
\left(\dfrac{f}{g}\right)(-1)=\dfrac{3(1)-4}{(1)-3(-1)-4}
\\\\
\left(\dfrac{f}{g}\right)(-1)=\dfrac{3-4}{1+3-4}
\\\\
\left(\dfrac{f}{g}\right)(-1)=\dfrac{-1}{0}
\\\\
\left(\dfrac{f}{g}\right)(-1)\text{ is undefined}
.\end{array}
