Answer
$\text{a) }
f(g(x))=35x+9
\\\text{b) }
g(f(x))=30x-33$
Work Step by Step
$\bf{\text{Solution Outline:}}$
With
\begin{array}{l}\require{cancel}
f(x)=
5x-6
\\g(x)=
7x+3
,\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(7x+3)
\\\\
f(g(x))=5(7x+3)-6
\\\\
f(g(x))=35x+15-6
\\\\
f(g(x))=35x+9
.\end{array}
Replacing $x$ with $f(x)$ in $g$, then
\begin{array}{l}\require{cancel}
g(f(x))=g(5x-6)
\\\\
g(f(x))=6(5x-6)+3
\\\\
g(f(x))=30x-36+3
\\\\
g(f(x))=30x-33
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
\text{a) }
f(g(x))=35x+9
\\\text{b) }
g(f(x))=30x-33
.\end{array}
