Question

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Explanation:

Step1: Identify invalid x for $f(x)$

Denominator of $f(x)$: $x-6=0 \implies x=6$

Step2: Identify invalid x for $g(x)$

Denominator of $g(x)$: $x+7=0 \implies x=-7$

Step3: Exclude x where $g(x)=0$

$g(x)=\frac{9}{x+7}$ can never equal 0 (numerator is 9≠0)

Step4: Combine excluded values

Domain excludes $x=6$ and $x=-7$

Answer:

B. The domain of $\frac{f}{g}$ is $(-\infty,-7) \cup (-7,6) \cup (6,\infty)$.