Answer
$\text{a) }
f(g(x))=4.2x-0.32
\\\\\text{b) }
g(f(x))=4.2x+17.6$
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}
replace $x$ with $g(x)$ in $f$ to find $f(g(x)).$ To find $g(f(x)),$ replace $x$ with $f(x)$ in $g.$
$\bf{\text{Solution Details:}}$
Replacing $x$ with $g(x)$ in $f,$ then
\begin{array}{l}\require{cancel}
f(g(x))=f(-7x-4.8)
\\\\
f(g(x))=-0.6(-7x-4.8)-3.2
\\\\
f(g(x))=4.2x+2.88-3.2
\\\\
f(g(x))=4.2x-0.32
.\end{array}
Replacing $x$ with $f(x)$ in $g.$ Hence,
\begin{array}{l}\require{cancel}
g(f(x))=g(-0.6x-3.2)
\\\\
g(f(x))=-7(-0.6x-3.2)-4.8
\\\\
g(f(x))=4.2x+22.4-4.8
\\\\
g(f(x))=4.2x+17.6
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
\text{a) }
f(g(x))=4.2x-0.32
\\\\\text{b) }
g(f(x))=4.2x+17.6
.\end{array}
