Final answer:
To calculate g(x) = f(2x) + 3 where f(x) = 2x², we substitute 2x into f(x) to get 8x² and then add 3, yielding g(x) = 8x² + 3.
Step-by-step explanation:
To find the function g(x) where g(x) = f(2x) + 3 and f(x) = 2x², we first substitute 2x into the function f. Doing so, we get f(2x) = 2(2x)² = 8x². Next, we add 3 to this result to find g(x):
g(x) = f(2x) + 3 = 8x² + 3.
This represents a parabolic function that has been vertically stretched by a factor of 8 and shifted upwards by 3 units.