Find the indicated function and write its domain in interval notation.
-$p ( x ) = x ^ { 2 } + 6 x , q ( x ) = \sqrt { 4 - x } , \left( \frac { q } { p } \right) ( x ) =$ ?
A) $\left( \frac { q } { p } \right) ( x ) = \frac { \sqrt { 4 - x } } { x ^ { 2 } + 6 x } ; ( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0,4 ]$
B) $\left( \frac { q } { p } \right) ( x ) = \frac { \sqrt { 4 - x } } { x ^ { 2 } + 6 x } ; ( - \infty , - 6 ) ( - 6,0 ) \cup ( 0 , \infty )$
C) $\left( \frac { q } { p } \right) ( x ) = \sqrt { \frac { 4 - x } { x ^ { 2 } + 6 x } } ; ( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0,4 )$
D) $\left( \frac { q } { p } \right) ( x ) = \sqrt { \frac { 4 - x } { x ^ { 2 } + 6 x } } ; ( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0 , \infty )$

Question

Quizplus · Accepted Answer

The correct function is $\frac { \sqrt { 4 - x } } { x ^ { 2 } + 6 x }$. The domain excludes $x = -6$ and $x = 0$ due to division by zero in $p(x)$, and $x > 4$ because the square root becomes imaginary. Thus, the domain is $(- \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0,4 ]$.

Find the Indicated Function and Write Its Domain in Interval p(x)=x2+6x,q(x)=4−x,(qp)(x)=p ( x ) = x ^ { 2 } + 6 x , q ( x ) = \sqrt { 4 - x } , \left( \frac { q } { p } \right) ( x ) =p(x)=x2+6x,q(x)=4−x​,(pq​)(x)=

Find the Indicated Function and Write Its Domain in Interval $p ( x ) = x ^ { 2 } + 6 x , q ( x ) = \sqrt { 4 - x } , \left( \frac { q } { p } \right) ( x ) =$