Answer
$\text{a) }
f(g(x))=3x^2+12x+35
\\\\\text{b) }
g(f(x))=9x^2+42x+55$
Work Step by Step
$\bf{\text{Solution Outline:}}$
With
\begin{array}{l}\require{cancel}
f(x)=
3x+5
\\g(x)=
x^2+4x+10
,\end{array}
replace $x$ with $g(x)$ in $f$ to find $f(g(x)).$ 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(x^2+4x+10)
\\\\
f(g(x))=3(x^2+4x+10)+5
\\\\
f(g(x))=3x^2+12x+30+5
\\\\
f(g(x))=3x^2+12x+35
.\end{array}
Replacing $x$ with $f(x)$ in $g.$ Hence,
\begin{array}{l}\require{cancel}
g(f(x))=g(3x+5)
\\\\
g(f(x))=(3x+5)^2+4(3x+5)+10
\\\\
g(f(x))=(9x^2+30x+25)+(12x+20)+10
\\\\
g(f(x))=9x^2+42x+55
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
\text{a) }
f(g(x))=3x^2+12x+35
\\\\\text{b) }
g(f(x))=9x^2+42x+55
.\end{array}
