Given functions f and g, perform the indicated operations.
-$$f ( x ) = \frac { 4 x } { x - 4 } , \quad g ( x ) = \frac { 5 } { x + 10 }$$
A) $( - \infty , - 10 )$ or $( - 10,4 )$ or $( 4 , \infty )$
B) $( - \infty , \infty )$
C) $( - \infty , - 4 )$ or $( - 4,10 )$ or $( 10 , \infty )$
D) $( - \infty , - 5 )$ or $( - 5 , - 4 )$ or $( - 4 , \infty )$

Question

Quizplus · Accepted Answer

The domain of $f(x) = \frac{4x}{x-4}$ excludes $x = 4$ because the denominator cannot be zero. The domain of $g(x) = \frac{5}{x+10}$ excludes $x = -10$ for the same reason. Therefore, the combined domain of $f$ and $g$ is all real numbers except $x = 4$ and $x = -10$, which corresponds to the intervals $(-\infty, -10)$, $(-10, 4)$, and $(4, \infty)$.

Given Functions F and G, Perform the Indicated Operations f(x)=4xx−4,g(x)=5x+10f ( x ) = \frac { 4 x } { x - 4 } , \quad g ( x ) = \frac { 5 } { x + 10 }f(x)=x−44x​,g(x)=x+105​

Given Functions F and G, Perform the Indicated Operations $f ( x ) = \frac { 4 x } { x - 4 } , \quad g ( x ) = \frac { 5 } { x + 10 }$