Consider the following functions. f(x) = 4x^2 + 5, g(x) = 6x Find (f circ g)(x) , (g circ f)(x), f(g(-3)),g(f(4))

Ralzereep9h 2022-10-21 Answered
Consider the following functions.
f ( x ) = 4 x 2 + 5 ,   g ( x ) = 6 x
Find ( f g ) ( x )       ,       ( g f ) ( x )       ,       f ( g ( 3 ) )       ,       g ( f ( 4 ) )
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Answers (1)

Szulikto
Answered 2022-10-22 Author has 22 answers
Step 1
Find ( f g ) ( x )
( f g ) ( x ) = f ( g ( x ) ) = f ( 6 x ) = 4 ( 6 x ) 2 + 5 = 4 ( 36 x 2 ) + 5 = 144 x 2 + 5 Find  ( g f ) ( x ) ( g f ) ( x ) = g ( f ( x ) ) = g ( 4 x 2 + 5 ) = 6 ( 4 x 2 + 5 ) = 24 x 2 + 30 Find  f ( g ( 3 ) ) f ( g ( 3 ) ) = f ( 6 ( ( 3 ) ) = f ( 18 ) = 4 ( 18 ) 2 + 5 = 4 ( 324 ) + 5 = 1296 + 5 = 1301 Find  g ( f ( 4 ) ) g ( f ( 4 ) ) = g ( 4 ( 4 ) 2 + 5 ) = g ( 4 ( 16 ) + 5 ) = g ( 64 + 5 ) = g ( 69 ) = 6 ( 69 ) = 414
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