Answer
$\text{a) }
f(g(x))=12x+13
\\\text{b) }
g(f(x))=12x-25$
Work Step by Step
$\bf{\text{Solution Outline:}}$
With
\begin{array}{l}\require{cancel}
f(x)=
3x-8
\\g(x)=
4x+7
,\end{array}
to find $
f(g(x))
,$ replace $x$ with $g(x)$ in $f.$ 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(4x+7)
\\\\
f(g(x))=3(4x+7)-8
\\\\
f(g(x))=12x+21-8
\\\\
f(g(x))=12x+13
.\end{array}
Replacing $x$ with $f(x)$ in $g$, then
\begin{array}{l}\require{cancel}
g(f(x))=g(3x-8)
\\\\
g(f(x))=4(3x-8)+7
\\\\
g(f(x))=12x-32+7
\\\\
g(f(x))=12x-25
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
\text{a) }
f(g(x))=12x+13
\\\text{b) }
g(f(x))=12x-25
.\end{array}
