If g ( x ) = 8 x + 4 and f ( x ) = 5 x 2 $-$ 9, find $( f \circ g ) ( 4 ) \text { and } ( g \circ f ) ( 4 )$ . Match each expression with the corresponding answer.
-$6,471$
A) $( f \circ g ) ( 4 )$
B) $( g \circ f ) ( 4 )$

Question

If g ( x ) = 8 x + 4 and f ( x ) = 5 x 2 $-$ 9, find $( f \circ g ) ( 4 ) \text { and } ( g \circ f ) ( 4 )$ . Match each expression with the corresponding answer.
-$6,471$ 
A) $( f \circ g ) ( 4 )$ 
B) $( g \circ f ) ( 4 )$

Quizplus · Accepted Answer

To find (f ∘ g)(4), we first evaluate g(4) by plugging in 4 for x in the definition of g(x):
g(4) = 8(4) + 4 = 36
Now we plug in g(4) for x in the definition of f(x):
f(g(4)) = f(36) = 5(36)^2 - 9 = 6,471

We cannot find (g ∘ f)(4) because f(x) is not defined for all real numbers, only for x in the domain of f. Since we do not know the domain of f or g, we cannot determine whether 4 is in the domain of f. Therefore, (g ∘ f)(4) is undefined.

If G ( X ) = 8 X + 4 −-−

If G ( X ) = 8 X + 4 $-$