Answer
$\text{a) }
f(g(x))=-323x+674
\\\text{b) }
g(f(x))=-323x+510$
Work Step by Step
$\bf{\text{Solution Outline:}}$
With
\begin{array}{l}\require{cancel}
f(x)=
19x+28
\\g(x)=
-17x+34
,\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(-17x+34)
\\\\
f(g(x))=19(-17x+34)+28
\\\\
f(g(x))=-323x+646+28
\\\\
f(g(x))=-323x+674
.\end{array}
Replacing $x$ with $f(x)$ in $g$, then
\begin{array}{l}\require{cancel}
g(f(x))=g(19x+28)
\\\\
g(f(x))=-17(19x+28)+34
\\\\
g(f(x))=-323x+476+34
\\\\
g(f(x))=-323x+510
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
\text{a) }
f(g(x))=-323x+674
\\\text{b) }
g(f(x))=-323x+510
.\end{array}
