Final answer:
To find the value of (fog)(-2), substitute -2 into the function g(x) and then substitute the result into the function f(x).
Step-by-step explanation:
To find the value of (fog)(-2), we need to substitute -2 into the function g(x) and then substitute the result into the function f(x).
Given that f(x) = 3x^2 + 6x + 11, let's first find g(-2):
g(x) = -13 ± √((13)^2 - 4 × 3 × (-10))
g(x) = -13 ± √(169 + 120)
g(x) = -13 ± √(289)
g(x) = -13 ± 17
Therefore, g(-2) = -13 + 17 = 4
Now, substitute g(-2) into f(x):
f(g(-2)) = 3(4)^2 + 6(4) + 11
f(g(-2)) = 3(16) + 24 + 11
f(g(-2)) = 48 + 24 + 11
f(g(-2)) = 83 + 11
f(g(-2)) = 94