Final answer:
To calculate g(f(3)), find f(3) first, which is constant at 23, and then apply it to g(x) to get g(23) = 48. However, as 48 isn't an option, there may be an error in the given functions or answer choices.
Step-by-step explanation:
To find the value of g(f(3)), first we need to find the value of f(3). The function f(x) is given by f(x) = 22 + 1. Since there's no x in the expression for f(x), it means that f(x) is a constant function and f(3) will be the same as f(x) for any value of x. Therefore, f(3) = 22 + 1 = 23.
Now that we have f(3) = 23, we can substitute this value into g(x). The function g(x) is given by g(x) = 2x + 2. Substituting f(3) into g(x), we get g(f(3)) = g(23), which simplifies to g(23) = 2(23) + 2 = 46 + 2 = 48.
However, as the answer 48 is not one of the provided options (A: 8, B: 10, C: 22, or D: 65), it appears there might have been a typo in the function f(x). If the function was f(x) = 2x + 1 instead, then f(3) would be 2(3) + 1 = 7, and subsequently g(f(3)) would be g(7) = 2(7) + 2 = 14 + 2 = 16. Still, 16 is not among the options, indicating a possible error in the question or the answer choices provided.