Final answer:
To find a point on the graph of the function g(x) = -f(2x) + 3, substitute the x-coordinate of the given point into the function and solve.
Step-by-step explanation:
To find a point on the graph of the function g(x) = -f(2x) + 3, we need to substitute the x-coordinate of the given point (4, 12) into the function g(x).
g(x) = -f(2x) + 3
g(4) = -f(2*4) + 3
g(4) = -f(8) +3
Since (4, 12) is a point on the graph of f(x), f(8) = 12. Substituting this value into g(4), we get:
g(4) = -12 + 3
g(4) = -9
Therefore, the point on the graph of g(x) is (4, -9).