Answer
$(fg)(-3)=144$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
(fg)(-3)
,$ 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 $
-3
.$
$\bf{\text{Solution Details:}}$
Since $(fg)(x)=f(x)g(x),$ then
\begin{array}{l}\require{cancel}
(fg)(x)=(x^2+3)(-2x+6)
\\\\
(fg)(x)=x^2(-2x)+x^2(6)+3(-2x)+3(6)
\\\\
(fg)(x)=-2x^3+6x^2-6x+18
.\end{array}
Substituting $x$ with $
-3
,$ then
\begin{array}{l}\require{cancel}
(fg)(-3)=-2(-3)^3+6(-3)^2-6(-3)+18
\\\\
(fg)(-3)=-2(-27)+6(9)-6(-3)+18
\\\\
(fg)(-3)=54+54+18+18
\\\\
(fg)(-3)=144
.\end{array}