Answer
$\text{a) }
g(x)-f(x)=18x-1
\\\\\text{b) }
f(x)g(x)=-77x^2+19x+6
\\\\\text{c) }
g(f(x))=-77x+35$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Substitute the given functions,
\begin{array}{l}\require{cancel}
f(x)=
-7x+3
\\g(x)=
11x+2
,\end{array}
into the required operations.
$\bf{\text{Solution Details:}}$
a)
\begin{array}{l}\require{cancel}
g(x)-f(x)=(11x+2)-(-7x+3)
\\\\
g(x)-f(x)=11x+2+7x-3
\\\\
g(x)-f(x)=18x-1
\end{array}
b)
\begin{array}{l}\require{cancel}
f(x)g(x)=(-7x+3)(11x+2)
\\\\
f(x)g(x)=-7x(11x)-7x(2)+3(11x)+3(2)
\\\\
f(x)g(x)=-77x^2-14x+33x+6
\\\\
f(x)g(x)=-77x^2+19x+6
\end{array}
c)
\begin{array}{l}\require{cancel}
g(f(x))=g(-7x+3)
\\\\
g(f(x))=11(-7x+3)+2
\\\\
g(f(x))=-77x+33+2
\\\\
g(f(x))=-77x+35
\end{array}
Therefore,
\begin{array}{l}\require{cancel}
\text{a) }
g(x)-f(x)=18x-1
\\\\\text{b) }
f(x)g(x)=-77x^2+19x+6
\\\\\text{c) }
g(f(x))=-77x+35
.\end{array}
