Find the domain of the function.
-$$f ( x ) = \frac { 1 } { x - 5 } + \frac { 4 } { x + 10 }$$
A) $( \infty , - 5 )$ or $( - 5,10 )$ or $( 10 , \infty )$
B) $( \infty , - 10 )$ or $( - 10,5 )$ or $( 5 , \infty )$
C) $( \infty , \infty )$
D) $( \infty , - 10 )$ or $( 5 , \infty )$

Question

Quizplus · Accepted Answer

The domain of the function excludes values that make the denominator zero. For $f(x) = \frac{1}{x-5} + \frac{4}{x+10}$, the denominators $x-5$ and $x+10$ cannot be zero, so $x \neq 5$ and $x \neq -10$. Thus, the domain is all real numbers except 5 and -10, which matches choice B.

Find the Domain of the Function f(x)=1x−5+4x+10f ( x ) = \frac { 1 } { x - 5 } + \frac { 4 } { x + 10 }f(x)=x−51​+x+104​

Find the Domain of the Function $f ( x ) = \frac { 1 } { x - 5 } + \frac { 4 } { x + 10 }$