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

The composition $f \circ g$ means applying $g$ first and then $f$. So, $g(x) = 9 - x$, and then $f(g(x)) = |(9-x)^2 + 1| = |x^2 - 18x + 81 + 1| = |x^2 - 18x + 82|$.

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