Final answer:
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.