Choose the one alternative that best completes the statement or answers the question.
Find the domain of the composite function f ° g.
-$$f ( x ) = x + 8 ; \quad g ( x ) = \frac { 4 } { x + 6 }$$
A) $\{ x \mid x \neq - 14 \}$
B) $\{ x \mid x \neq - 6 \}$
C) $\{ x \mid x \neq - 6 , x \neq - 8 \}$
D) $\{ x \mid x$ is any real number $\}$

Question

Quizplus · Accepted Answer

The domain of the composite function $f \circ g$ is determined by the domain of $g(x)$, since $g(x)$ is the inner function. $g(x) = \frac{4}{x + 6}$ is undefined when $x + 6 = 0$, or $x = -6$. Therefore, the domain of $f \circ g$ is all real numbers except $x \neq -6$.

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