Final answer:
To find F(G(x)), substitute G(x) into the function f(x) and perform the necessary calculations.
Step-by-step explanation:
To find F(G(x)), we need to substitute G(x) into the function f(x). So, we replace x in f(x) with G(x).
f(G(x)) = 3(G(x))² + 1.
Now, we substitute G(x) = 2x - 3 into the equation:
f(G(x)) = 3(2x - 3)² + 1.
Simplifying further:
f(G(x)) = 3(4x² - 12x + 9) + 1.
f(G(x)) = 12x² - 36x + 28.
Therefore, F(G(x)) = 12x² - 36x + 28.