Find the indicated function and write its domain in interval notation.
-$$r ( x ) = | - 3 x - 7 | , n ( x ) = x + 4 , ( r \circ n ) ( x ) = ?$$
A) $( r \circ n ) ( x ) = | - 3 x - 19 |$; domain: $( - \infty , \infty )$
B) $( r \circ n ) ( x ) = | - 3 x - 7 | + 4$; domain: $( - \infty , \infty )$
C) $( r \circ n ) ( x ) = | - 3 x - 19 | ;$ domain: $\left( - \infty , - \frac { 19 } { 3 } \right)$
D) $( r \circ n ) ( x ) = | - 3 x - 7 | + 4 ;$ domain: $\left( - \infty , - \frac { 7 } { 3 } \right)$

Question

Quizplus · Accepted Answer

The composition $(r \circ n)(x)$ means applying $n(x)$ first, then $r$ to the result. So, $n(x) = x + 4$, and then $r(n(x)) = | -3(x + 4) - 7 | = |-3x - 12 - 7| = |-3x - 19|$. The domain of both $r(x)$ and $n(x)$ is all real numbers, $(-\infty, \infty)$, because there are no restrictions like division by zero or square roots of negative numbers.

Find the Indicated Function and Write Its Domain in Interval r(x)=∣−3x−7∣,n(x)=x+4,(r∘n)(x)=?r ( x ) = | - 3 x - 7 | , n ( x ) = x + 4 , ( r \circ n ) ( x ) = ?r(x)=∣−3x−7∣,n(x)=x+4,(r∘n)(x)=?

Find the Indicated Function and Write Its Domain in Interval $r ( x ) = | - 3 x - 7 | , n ( x ) = x + 4 , ( r \circ n ) ( x ) = ?$