Find $f \circ g$ . $f ( x ) = \left| x ^ { 2 } + 1 \right| \quad g ( x ) = 9 - x$
A) $$( f \circ g ) ( x ) = \left| x ^ { 2 } - 18 x + 82 \right|$$
B) $( f \circ g ) ( x ) = \left| x ^ { 2 } + 82 \right|$
C) $( f \circ g ) ( x ) = \left| 8 - x ^ { 2 } \right|$
D) $( f \circ g ) ( x ) = \left| 10 - x ^ { 2 } \right|$
E) $$( f \circ g ) ( x ) = 9 - \left| x ^ { 2 } + 1 \right|$$

Question

Find $f \circ g$ .​ $f ( x ) = \left| x ^ { 2 } + 1 \right| \quad g ( x ) = 9 - x$ ​
A) $$( f \circ g ) ( x ) = \left| x ^ { 2 } - 18 x + 82 \right|$$
B) $( f \circ g ) ( x ) = \left| x ^ { 2 } + 82 \right|$
C) $( f \circ g ) ( x ) = \left| 8 - x ^ { 2 } \right|$
D) $( f \circ g ) ( x ) = \left| 10 - x ^ { 2 } \right|$
E) $$( f \circ g ) ( x ) = 9 - \left| x ^ { 2 } + 1 \right|$$

Quizplus · Accepted Answer

To find $f \circ g$, we substitute $g(x) = 9 - x$ into $f(x)$, resulting in $f(g(x)) = \left| (9 - x)^2 + 1 \right| = \left| 81 - 18x + x^2 + 1 \right| = \left| x^2 - 18x + 82 \right|$.

Find f∘gf \circ gf∘g ​ f(x)=∣x2+1∣g(x)=9−xf ( x ) = \left| x ^ { 2 } + 1 \right| \quad g ( x ) = 9 - xf(x)=​x2+1​g(x)=9−x

Find $f \circ g$ $f ( x ) = \left| x ^ { 2 } + 1 \right| \quad g ( x ) = 9 - x$