Question

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

f(x) = 3x² – 3x – 7
-
g(x) = -3x - 10

Answer 1

To find (g∘f)(-2), calculate f(-2) and then apply g to that result. After evaluating the functions step by step, the answer is -43.

Step-by-step explanation:

To find the value of (g ∘ f)(-2), you first apply f to -2, then you apply g to the result of f(-2). First, let's compute f(-2):

f(-2) = 3(-2)² - 3(-2) - 7
= 3(4) + 6 - 7
= 12 + 6 - 7
= 11

Now we apply g to f(-2):

g(11) = -3(11) - 10
= -33 - 10
= -43

Therefore, (g ∘ f)(-2) is -43.