Answer
$(fg)(x)=3x^4-9x^3-16x^2+12x+16$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the expression, $
(fg)(x)
,$ 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.
$\bf{\text{Solution Details:}}$
Using $(fg)(x)=f(x)g(x),$ then
\begin{array}{l}\require{cancel}
(fg)(x)=(3x^2-4)(x^2-3x-4)
\\\\
(fg)(x)=3x^2(x^2)+3x^2(-3x)+3x^2(-4)-4(x^2)-4(-3x)-4(-4)
\\\\
(fg)(x)=3x^4-9x^3-12x^2-4x^2+12x+16
\\\\
(fg)(x)=3x^4-9x^3-16x^2+12x+16
.\end{array}