Find (gºf)(4) when f(x)
f)(4) when f(x) = 4x - 2 and g(x)
-6x² - 86 - 8.

(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