Answer
$(f-g)(4)=44$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the expression, $
(f-g)(4)
,$ 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 $4.$
$\bf{\text{Solution Details:}}$
Using $(f-g)(x)=f(x)-g(x),$ then
\begin{array}{l}\require{cancel}
(f-g)(x)=(3x^2-4)-(x^2-3x-4)
\\\\
(f-g)(x)=3x^2-4-x^2+3x+4
\\\\
(f-g)(x)=(3x^2-x^2)+3x+(-4+4)
\\\\
(f-g)(x)=2x^2+3x
.\end{array}
Sustituting $x$ with $4,$ then
\begin{array}{l}\require{cancel}
(f-g)(4)=2(4)^2+3(4)
\\\\
(f-g)(4)=2(16)+3(4)
\\\\
(f-g)(4)=32+12
\\\\
(f-g)(4)=44
.\end{array}
