Answer
$\text{a) }
f(g(2))=-209
\\\\\text{b) }
f(6)-g(6)=104
\\\\\text{c) }
\dfrac{f(6)}{g(6)}=-\dfrac{67}{37}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Substitute the given functions,
\begin{array}{l}\require{cancel}
f(x)=
12x-5
\\g(x)=
-5x-7
,\end{array}
into the required operations.
$\bf{\text{Solution Details:}}$
a)
\begin{array}{l}\require{cancel}
f(g(x))=f(-5x-7)
\\\\
f(g(2))=f(-5(2)-7)
\\\\
f(g(2))=f(-10-7)
\\\\
f(g(2))=f(-17)
\\\\
f(g(2))=12(-17)-5
\\\\
f(g(2))=-204-5
\\\\
f(g(2))=-209
\end{array}
b)
\begin{array}{l}\require{cancel}
f(x)-g(x)=(12x-5)-(-5x-7)
\\\\
f(6)-g(6)=(12(6)-5)-(-5(6)-7)
\\\\
f(6)-g(6)=(72-5)-(-30-7)
\\\\
f(6)-g(6)=(67)-(-37)
\\\\
f(6)-g(6)=67+37
\\\\
f(6)-g(6)=104
\end{array}
c)
\begin{array}{l}\require{cancel}
\dfrac{f(x)}{g(x)}=\dfrac{12x-5}{-5x-7}
\\\\
\dfrac{f(6)}{g(6)}=\dfrac{12(6)-5}{-5(6)-7}
\\\\
\dfrac{f(6)}{g(6)}=\dfrac{72-5}{-30-7}
\\\\
\dfrac{f(6)}{g(6)}=\dfrac{67}{-37}
\\\\
\dfrac{f(6)}{g(6)}=-\dfrac{67}{37}
\end{array}
Therefore,
\begin{array}{l}\require{cancel}
\text{a) }
f(g(2))=-209
\\\\\text{b) }
f(6)-g(6)=104
\\\\\text{c) }
\dfrac{f(6)}{g(6)}=-\dfrac{67}{37}
.\end{array}
