Answer
$\text{a) }
(f\circ g)(-3)=29.08
\\\\\text{b) }
(g\circ f)(-3)=47$
Work Step by Step
$\bf{\text{Solution Outline:}}$
With
\begin{array}{l}\require{cancel}
f(x)=
-0.6x-3.2
\\g(x)=
-7x-4.8
,\end{array}
to find $
(f\circ g)(7)
,$ find first $
g(7)
.$ Then substitute the result in $f.$
To find $
(g\circ f)(7)
,$ find first $
f(7)
.$ Then substitute the result in $g.$
$\bf{\text{Solution Details:}}$
a) Since $(f\circ g)(7)=f(g(7)),$ find first $g(7).$ That is
\begin{array}{l}\require{cancel}
g(x)=-7x-4.8
\\\\
g(7)=-7(7)-4.8
\\\\
g(7)=-49-4.8
\\\\
g(7)=-53.8
.\end{array}
Replacing $x$ with the result above in $f$ results to
\begin{array}{l}\require{cancel}
f(x)=-0.6x-3.2
\\\\
f(-53.8)=-0.6(-53.8)-3.2
\\\\
f(-53.8)=32.28-3.2
\\\\
f(-53.8)=29.08
.\end{array}
Hence, $
(f\circ g)(7)=f(g(7))=29.08
.$
b) Since $(g\circ f)(7)=g(f(7)),$ find first $f(7).$ Replacing $x$ with $
7
$ in $f$ results to
\begin{array}{l}\require{cancel}
f(x)=-0.6x-3.2
\\\\
f(7)=-0.6(7)-3.2
\\\\
f(7)=-4.2-3.2
\\\\
f(7)=-7.4
.\end{array}
Replacing $x$ with the result above in $g$ results to
\begin{array}{l}\require{cancel}
g(x)=-7x-4.8
\\\\
g(-7.4)=-7(-7.4)-4.8
\\\\
g(-7.4)=51.8-4.8
\\\\
g(-7.4)=47
.\end{array}
Hence, $
(g\circ f)(7)=g(f(7))=47
.$
Therefore,
\begin{array}{l}\require{cancel}
\text{a) }
(f\circ g)(-3)=29.08
\\\\\text{b) }
(g\circ f)(-3)=47
.\end{array}