Final answer:
To find g(x) = -2f(-2) + 3, substitute -2 for x in the function f(x) = x^2, and then apply the given equation.
Step-by-step explanation:
The function rule tells the relationship between the input or domain and the output or range. To find g(x) = -2f(-2) + 3, we need to substitute -2 for x in the function f(x) = x^2 and then apply the given equation.
Step 1: Substitute -2 for x in f(x) = x^2:
f(-2) = (-2)^2
f(-2) = 4
Step 2: Apply g(x) = -2f(-2) + 3:
g(x) = -2(4) + 3
g(x) = -8 + 3
g(x) = -5