Final answer:
To find g(g(-3)), we first evaluate g(-3) by substituting -3 in the expression for g(x), resulting in 7. Then, we substitute 7 back into g(x) to get g(7), which simplifies to 27. Therefore, g(g(-3)) equals 27.
Step-by-step explanation:
The question asks to evaluate a nested function g(g(-3)) given the expression g(x) = x² - 2x - 8. First, we find g(-3) by substituting -3 into the given expression, resulting in g(-3) = (-3)² - 2(-3) - 8. Simplifying this gives us g(-3) = 9 + 6 - 8, which equals 7. Next, we evaluate g(g(-3)) by replacing x with 7 in the expression g(x), leading to g(7) = 7² - 2(7) - 8.
Continuing this process, we simplify g(7) to obtain g(7) = 49 - 14 - 8, which simplifies to g(7) = 27.
Finally, we conclude that g(g(-3)) = g(7) = 27.