Perform the requested operation or operations. Find the domain of each.
-$f ( x ) = \sqrt { x + 8 }$ and $g ( x ) = | x - 6 |$
Find $f g$.
A) $| x - 6 | \sqrt { x + 8 } ;$ domain: $( 6 , \infty )$
B) $\sqrt { x ^ { 2 } + 2 x - 48 }$; domain: $( - \infty , - 8 ) \cup ( 6 , \infty )$
C) $\left| x ^ { 2 } + 2 x - 48 \right|$; domain: $( - \infty , \infty )$
D) $| x - 6 | \sqrt { x + 8 }$; domain: $( - 8 , \infty )$

Question

Quizplus · Accepted Answer

The composition $f(g(x))$ results in $|x - 6|\sqrt{x + 8}$. The domain of $f(x) = \sqrt{x + 8}$ is $x \geq -8$ because the expression under the square root must be non-negative. The domain of $g(x) = |x - 6|$ is all real numbers, $(-\infty, \infty)$, because the absolute value function is defined for all real numbers. The domain of the composition is determined by the requirement that $x + 8 \geq 0$, which simplifies to $x \geq -8$. Therefore, the domain of the composition is $(-8, \infty)$.

Perform the Requested Operation or Operations f(x)=x+8f ( x ) = \sqrt { x + 8 }f(x)=x+8​

Perform the Requested Operation or Operations $f ( x ) = \sqrt { x + 8 }$