Final answer:
The value of f(g(-2)) is found by first evaluating g(-2), which is 6, and then using this result to evaluate f(6). The final result is -13, which is not in the provided options.
Step-by-step explanation:
To find the value of f(g(-2)), you first need to calculate g(-2) and then evaluate f at the result of g(-2).
Step 1: Evaluate g(-2)
Given g(x) = x² + 2, plug -2 in for x:
g(-2) = (-2)² + 2 = 4 + 2 = 6
Step 2: Evaluate f(g(-2)) or f(6)
Now, take the result from step 1 and plug it into the function f:
Given f(x) = -1/2x² + 5, plug 6 in for x:
f(6) = -½(6)² + 5 = -½(36) + 5 = -18 + 5 = -13
Therefore, the value of f(g(-2)) is -13, which is not listed in the provided multiple-choice options.