For the pair of functions, determine the domain of f + g.
-$$f ( x ) = \frac { 5 x } { x - 7 } , g ( x ) = \frac { 3 } { x + 1 }$$
A) $( \infty , \infty )$
B) $( \infty , - 1 )$ or $( - 1,7 )$ or $( 7 , \infty )$
C) $( \infty , - 1 )$ or $( 7 , \infty )$
D) $( \infty , - 7 )$ or $( - 7,1 )$ or $( 1 , \infty )$

Question

For the pair of functions, determine the domain of f + g.
-$$f ( x ) = \frac { 5 x } { x - 7 } , g ( x ) = \frac { 3 } { x + 1 }$$
A) $( \infty , \infty )$
B) $(  \infty , - 1 )$ or $( - 1,7 )$ or $( 7 , \infty )$
C) $( \infty , - 1 )$ or $( 7 , \infty )$
D) $( \infty , - 7 )$ or $( - 7,1 )$ or $( 1 , \infty )$

Quizplus · Accepted Answer

The domain of $f + g$ is determined by the values of $x$ for which both $f(x)$ and $g(x)$ are defined. For $f(x) = \frac{5x}{x-7}$, $x$ cannot be 7 because it would make the denominator zero. For $g(x) = \frac{3}{x+1}$, $x$ cannot be -1 for the same reason. Therefore, the domain excludes -1 and 7, making the correct domain $(-\infty, -1)$, $(-1, 7)$, and $(7, \infty)$.

For the Pair of Functions, Determine the Domain of F f(x)=5xx−7,g(x)=3x+1f ( x ) = \frac { 5 x } { x - 7 } , g ( x ) = \frac { 3 } { x + 1 }f(x)=x−75x​,g(x)=x+13​

For the Pair of Functions, Determine the Domain of F $f ( x ) = \frac { 5 x } { x - 7 } , g ( x ) = \frac { 3 } { x + 1 }$