Find the domain of the composite function f g. Write the domain in interval notation.
-$$f ( x ) = x + 3 , g ( x ) = \frac { 3 } { x + 6 }$$
A) $( - \infty , - 6 ) \cup ( - 6 , - 3 ) \cup ( - 3 , \infty )$
B) $( - \infty , - 9 ) \cup ( - 9 , \infty )$
C) $( - \infty , \infty )$
D) $( - \infty , - 6 ) \cup ( - 6 , \infty )$

Question

Quizplus · Accepted Answer

The domain of $g(x) = \frac{3}{x+6}$ excludes $x = -6$ because the denominator cannot be zero. The function $f(x) = x + 3$ does not introduce any additional restrictions, so the domain of the composite function $f(g(x))$ is all real numbers except $x = -6$, which is option D: $(- \infty , - 6 ) \cup ( - 6 , \infty )$.

Find the Domain of the Composite Function F G f(x)=x+3,g(x)=3x+6f ( x ) = x + 3 , g ( x ) = \frac { 3 } { x + 6 }f(x)=x+3,g(x)=x+63​

Find the Domain of the Composite Function F G $f ( x ) = x + 3 , g ( x ) = \frac { 3 } { x + 6 }$