Find $f \circ g$.
$f ( x ) = \left| x ^ { 2 } - 6 \right| \quad g ( x ) = - 9 - x$
A) $( f \circ g ) ( x ) = \left| x ^ { 2 } + 18 x + 75 \right|$
B) $( f \circ g ) ( x ) = \left| x ^ { 2 } + 75 \right|$
C) $( f \circ g ) ( x ) = \left| - 3 - x ^ { 2 } \right|$
D) $( f \circ g ) ( x ) = \left| - 15 - x ^ { 2 } \right|$
E) $( f \circ g ) ( x ) = - 9 - \left| x ^ { 2 } - 6 \right|$

Question

Quizplus · Accepted Answer

To find $f \circ g$, we substitute $g(x) = -9 - x$ into $f(x)$, resulting in $f(g(x)) = \left| (-9 - x)^2 - 6 \right| = \left| x^2 + 18x + 81 - 6 \right| = \left| x^2 + 18x + 75 \right|$.

Find f∘gf \circ gf∘g f(x)=∣x2−6∣g(x)=−9−xf ( x ) = \left| x ^ { 2 } - 6 \right| \quad g ( x ) = - 9 - xf(x)=​x2−6​g(x)=−9−x

Find $f \circ g$ $f ( x ) = \left| x ^ { 2 } - 6 \right| \quad g ( x ) = - 9 - x$