Answer
$\text{a) }
f(g(2))=28
\\\\\text{b) }
g(f(2))=-1088$
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(2))
,$ find first $
g(2)
.$ Then substitute the result in $f.$
To find $
g(f(2))
,$ find first $
f(2)
.$ Then substitute the result in $g.$
$\bf{\text{Solution Details:}}$
a) Replacing $x$ with $
2
$ in $g$ results to
\begin{array}{l}\require{cancel}
g(x)=-17x+34
\\\\
g(2)=-17(2)+34
\\\\
g(2)=-34+34
\\\\
g(2)=0
.\end{array}
Replacing $x$ with the result above in $f$ results to
\begin{array}{l}\require{cancel}
f(x)=19x+28
\\\\
f(0)=19(0)+28
\\\\
f(0)=0+28
\\\\
f(0)=28
.\end{array}
Hence, $
f(g(2))=28
.$
b) Replacing $x$ with $
2
$ in $f$ results to
\begin{array}{l}\require{cancel}
f(x)=19x+28
\\\\
f(2)=19(2)+28
\\\\
f(2)=38+28
\\\\
f(2)=66
.\end{array}
Replacing $x$ with the result above in $g$ results to
\begin{array}{l}\require{cancel}
g(x)=-17x+34
\\\\
g(66)=-17(66)+34
\\\\
g(66)=-1122+34
\\\\
g(66)=-1088
.\end{array}
Hence, $
g(f(2))=-1088
.$
Therefore,
\begin{array}{l}\require{cancel}
\text{a) }
f(g(2))=28
\\\\\text{b) }
g(f(2))=-1088
.\end{array}
