Final answer:
To calculate f(g(f(-2))), you first find f(-2), then use this result as the input for g(x), and finally use the result as the input for f(x) again, yielding a final result of 54.
Step-by-step explanation:
To calculate f(g(f(-2))), we need to substitute the value of -2 into the functions f(x) and g(x) step by step.
- Start with f(-2):
f(-2) = 2(-2) - 6
f(-2) = -4 - 6
f(-2) = -10 - Next, substitute the result of f(-2) into g(x):
g(f(-2)) = -4(-10) - 10
g(f(-2)) = 40 - 10
g(f(-2)) = 30 - Finally, substitute the result of g(f(-2)) into f(x):
f(g(f(-2))) = 2(30) - 6
f(g(f(-2))) = 60 - 6
f(g(f(-2))) = 54
Therefore, f(g(f(-2))) = 54.