Answer:
(g°f)(4) = -1296
Step-by-step explanation:
It is given that:
g(x) = -6x² - 86x - 8
f(x) = 4x - 2
First find the equation of (g°f)
(g°f) = g [ f (x) ]
(g°f) = g [ 4x-2 ]
Substitute 4x-2 for x in formula of g(x)
g(x) = -6x² - 86x - 8
g(4x-2) = -6(4x - 2)² -8(4x - 2) - 8
g(4x-2) = -6(16x² + 4 - 2(4x)(2)) - 32x + 16 - 8
g(4x-2) = -96x² - 24 +96x - 32x + 16 - 8
g(4x-2) = -96x² + 64x - 16
(g°f)(x) = -96x² + 64x - 16
Substitute x=4 into the equation:
(g°f)(4) = -96(4)² + 64(4) - 16
(g°f)(4) = -1296