Write the domain of the rational function in interval notation. $$k ( x ) = \frac { x ( x + 7 ) } { x ( x - 12 ) ( x + 7 ) }$$
A) $( - \infty , 12 ) \cup ( 12 , \infty )$
B) $( - \infty , - 7 ) \cup ( - 7,0 ) \cup ( 0,12 ) \cup ( 12 , \infty )$
C) $( - \infty , - 7 ) \cup ( - 7,0 ) \cup ( 0 , \infty )$
D) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The domain of a rational function is all real numbers except where the denominator is equal to zero. In this function, the denominator is $x(x-12)(x+7)$, which is zero when $x = 0$, $x = 12$, or $x = -7$. Therefore, the domain excludes these values, leading to the intervals $( - \infty , - 7 ) \cup ( - 7,0 ) \cup ( 0,12 ) \cup ( 12 , \infty )$.

Write the Domain of the Rational Function in Interval Notation k(x)=x(x+7)x(x−12)(x+7)k ( x ) = \frac { x ( x + 7 ) } { x ( x - 12 ) ( x + 7 ) }k(x)=x(x−12)(x+7)x(x+7)​

Write the Domain of the Rational Function in Interval Notation $k ( x ) = \frac { x ( x + 7 ) } { x ( x - 12 ) ( x + 7 ) }$