Find the domain of the function.
-$$f ( x ) = \frac { 1 } { x - 6 } + \frac { 4 } { x + 12 }$$
A) $( \infty , \infty )$
B) $( \infty , - 6 )$ or $( - 6,12 )$ or $( 12 , \infty )$
C) $( \infty , - 12 )$ or $( 6 , \infty )$
D) $( \infty , - 12 )$ or $( - 12,6 )$ or $( 6 , \infty )$

Question

Quizplus · Accepted Answer

The domain of the function excludes values that make the denominator zero. For $f(x) = \frac{1}{x-6} + \frac{4}{x+12}$, the denominators $x-6$ and $x+12$ cannot be zero, so $x \neq 6$ and $x \neq -12$. This results in the domain being all real numbers except $6$ and $-12$, correctly represented in option D.

Find the Domain of the Function f(x)=1x−6+4x+12f ( x ) = \frac { 1 } { x - 6 } + \frac { 4 } { x + 12 }f(x)=x−61​+x+124​

Find the Domain of the Function $f ( x ) = \frac { 1 } { x - 6 } + \frac { 4 } { x + 12 }$