Answer
$\text{a) }
f(3)+g(3)=-15
\\\\\text{b) }
f(4)g(4)=-420
\\\\\text{c) }
f(g(7))=-134$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Substitute the given functions,
\begin{array}{l}\require{cancel}
f(x)=
-9x+1
\\g(x)=
x+8
,\end{array}
into the required operations.
$\bf{\text{Solution Details:}}$
a)
\begin{array}{l}\require{cancel}
f(x)+g(x)=(-9x+1)+(x+8)
\\\\
f(3)+g(3)=(-9(3)+1)+((3)+8)
\\\\
f(3)+g(3)=(-27+1)+(3+8)
\\\\
f(3)+g(3)=-26+11
\\\\
f(3)+g(3)=-15
\end{array}
b)
\begin{array}{l}\require{cancel}
f(x)g(x)=(-9x+1)(x+8)
\\\\
f(4)g(4)=(-9(4)+1)((4)+8)
\\\\
f(4)g(4)=(-36+1)(4+8)
\\\\
f(4)g(4)=(-35)(12)
\\\\
f(4)g(4)=-420
\end{array}
c)
\begin{array}{l}\require{cancel}
f(g(x))=f(x+8)
\\\\
f(g(7))=f(7+8)
\\\\
f(g(7))=f(15)
\\\\
f(g(7))=-9(15)+1
\\\\
f(g(7))=-135+1
\\\\
f(g(7))=-134
\end{array}
Therefore,
\begin{array}{l}\require{cancel}
\text{a) }
f(3)+g(3)=-15
\\\\\text{b) }
f(4)g(4)=-420
\\\\\text{c) }
f(g(7))=-134
.\end{array}
