Find the domain of the composite function f $f ^ { \circ } g $
-$$f ( x ) = \frac { x } { x + 7 } ; \quad g ( x ) = \frac { 7 } { x + 5 }$$
A) $\{ x \mid x \neq - 5 , x \neq - 6 \}$
B) $\{ x \mid x \neq 0 , x \neq - 5 , x \neq - 6 \}$
C) $\{ x \mid x$ is any real number $\}$
D) $\{ x \mid x \neq - 5 , x \neq - 7 \}$

Question

Quizplus · Accepted Answer

The domain of $g(x) = \frac{7}{x+5}$ excludes $x = -5$ to avoid division by zero. For $f(g(x))$, we substitute $g(x)$ into $f(x)$, resulting in $f\left(\frac{7}{x+5}\right) = \frac{\frac{7}{x+5}}{\frac{7}{x+5} + 7}$. Simplifying the denominator to avoid division by zero, we find $x \neq -6$ in addition to $x \neq -5$. Thus, the domain excludes $x = -5$ and $x = -6$.

Find the Domain of the Composite Function F f∘gf ^ { \circ } g f∘g

Find the Domain of the Composite Function F $f ^ { \circ } g$