Final answer:
To calculate fog(-5), evaluate g(-5) first, which is 45, and then apply this to f(x) to get 1930. The provided options do not include this correct result, indicating a potential error in the question or options.
Step-by-step explanation:
To find fog(-5), we first need to evaluate g(-5) and then apply the result to f(x). Given g(x) = x² + 20, we find:
g(-5) = (-5)² + 20 = 25 + 20 = 45.
Now we apply this result to f(x) = x² - 2x - 5, so we get:
f(g(-5)) = f(45) = 45² - 2(45) - 5 = 2025 - 90 - 5 = 1930.
Therefore, fog(-5) is equal to 1930. None of the options A) 420, B) -420, C) 400, or D) -400 match this result, so there might be a typo in the question or the options provided.