Final answer:
To find (f o g)(-8), first calculate g(-8) equal to -288, then plug this into f(x) to get f(-288) equal to 2014.
Step-by-step explanation:
To find the composite function (f o g)(-8), you first need to calculate g(-8) and then apply the result to the function f. Let's start by finding g(-8).
Given g(x) = - 4x² + 3x – 8, we substitute x with -8:
g(-8) = - 4(-8)² + 3(-8) – 8
g(-8) = - 4(64) - 24 - 8
g(-8) = - 256 - 24 - 8
g(-8) = - 288
Now we have determined that g(-8) is -288, we can proceed to find (f o g)(-8), which means plugging g(-8) into f(x):
Given f(x) = - 7x - 2, substitute x with -288:
f(g(-8)) = f(-288)
f(-288) = - 7(-288) - 2
f(-288) = 2016 - 2
f(-288) = 2014
So, the result of the composite function (f o g)(-8) is 2014.