Answer
$\text{a) }
f(g(4))=48
\\\\\text{b) }
g(f(4))=528$
Work Step by Step
$\bf{\text{Solution Outline:}}$
With
\begin{array}{l}\require{cancel}
f(x)=
5x-2
\\g(x)=
2x^2-7x+6
,\end{array}
to find $
f(g(4))
,$ find first $
g(4)
.$ Then substitute the result in $f.$
To find $
g(f(4))
,$ find first $
f(4)
.$ Then substitute the result in $g.$
$\bf{\text{Solution Details:}}$
a) Replacing $x$ with $
4
$ in $g$ results to
\begin{array}{l}\require{cancel}
g(x)=2x^2-7x+6
\\\\
g(4)=2(4)^2-7(4)+6
\\\\
g(4)=2(16)-28+6
\\\\
g(4)=32-28+6
\\\\
g(4)=10
.\end{array}
Replacing $x$ with the result above in $f$ results to
\begin{array}{l}\require{cancel}
f(x)=5x-2
\\\\
f(10)=5(10)-2
\\\\
f(10)=50-2
\\\\
f(10)=48
.\end{array}
Hence, $
f(g(4))=48
.$
b) Replacing $x$ with $
4
$ in $f$ results to
\begin{array}{l}\require{cancel}
f(x)=5x-2
\\\\
f(4)=5(4)-2
\\\\
f(4)=20-2
\\\\
f(4)=18
.\end{array}
Replacing $x$ with the result above in $g$ results to
\begin{array}{l}\require{cancel}
g(x)=2x^2-7x+6
\\\\
g(18)=2(18)^2-7(18)+6
\\\\
g(18)=2(324)-126+6
\\\\
g(18)=648-126+6
\\\\
g(18)=528
.\end{array}
Hence, $
g(f(4))=528
.$
Therefore,
\begin{array}{l}\require{cancel}
\text{a) }
f(g(4))=48
\\\\\text{b) }
g(f(4))=528
.\end{array}