Find the domain of the composite function f∘g.
-$$f ( x ) = \frac { 5 } { x + 9 } , \quad g ( x ) = x + 5$$
A) $( - \infty , - 14 )$ or $( - 14 , \infty )$
B) $( - \infty , - 9 )$ or $( - 9 , \infty )$
C) $( - \infty , - 9 )$ or $( - 9 , - 5 )$ or $( - 5 , \infty )$
D) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The composite function $f(g(x)) = \frac{5}{(x+5)+9}$ simplifies to $\frac{5}{x+14}$. The denominator cannot be zero, so $x+14 \neq 0$, which means $x \neq -14$. Therefore, the domain is all real numbers except -14.

Find the Domain of the Composite Function F∘g f(x)=5x+9,g(x)=x+5f ( x ) = \frac { 5 } { x + 9 } , \quad g ( x ) = x + 5f(x)=x+95​,g(x)=x+5

Find the Domain of the Composite Function F∘g $f ( x ) = \frac { 5 } { x + 9 } , \quad g ( x ) = x + 5$