Answer
$\text{a) }
f(x)g(x)=27x^2+69x+14
\\\\\text{b) }
f(x)+g(x)=12x+9
\\\\\text{c) }
f(g(x))=27x+65$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Substitute the given functions,
\begin{array}{l}\require{cancel}
f(x)=
9x+2
\\g(x)=
3x+7
,\end{array}
into the required operations.
$\bf{\text{Solution Details:}}$
a)
\begin{array}{l}\require{cancel}
f(x)g(x)=(9x+2)(3x+7)
\\\\
f(x)g(x)=9x(3x)+9x(7)+2(3x)+2(7)
\\\\
f(x)g(x)=27x^2+63x+6x+14
\\\\
f(x)g(x)=27x^2+69x+14
.\end{array}
b)
\begin{array}{l}\require{cancel}
f(x)+g(x)=(9x+2)+(3x+7)
\\\\
f(x)+g(x)=12x+9
.\end{array}
c)
\begin{array}{l}\require{cancel}
f(g(x))=f(3x+7)
\\\\
f(g(x))=9(3x+7)+2
\\\\
f(g(x))=27x+63+2
\\\\
f(g(x))=27x+65
.\end{array}
Therefore,
\begin{array}{l}\require{cancel}
\text{a) }
f(x)g(x)=27x^2+69x+14
\\\\\text{b) }
f(x)+g(x)=12x+9
\\\\\text{c) }
f(g(x))=27x+65
.\end{array}
