Question

Given the definitions of f(x) and g(2) below, find the value of (gof)(-8).

f(x) = -x – 8
g(x) = x2 – 3x + 2

Answer 1

To find (gof)(-8), first calculate f(-8) which is 0, and then substitute this into g(x) to get g(0), which equals 2. Therefore, the value of (gof)(-8) is 2.

Step-by-step explanation:

The student is asking to find the value of the composition of two functions, denoted as (gof)(-8). This means we want to find the value of g(f(x)) when x is -8. We start by finding the value of f(-8) using the given function f(x) = -x – 8, and then we will substitute this into g(x) and evaluate it.

1. First calculate f(-8):
   f(-8) = -(-8) – 8 = 8 – 8 = 0.
2. Then substitute this value into g(x):
   g(0) = 0² – 3·0 + 2,
   
   which simplifies to 2.
3. Therefore, (gof)(-8) = 2.