Answer: C

To determine whether f(f(2)) = 16 for a given function, two steps are required. First, evaluate f(2). Then, once you know the value of f(2), plug that in, and evaluate the function using that value of x. For instance, take choice (B). f(2) = x + 7 = 9. Now that you know that f(2) = 9, f(f(2)) is equivalent to f(9), or 9 + 7 = 16. We've established that if f(x) = x + 7, f(f(2)) = 16. Now check the other choices:
(A) If f(x) = 16, whatever the value of x, the function equals 16. That means: f(2) = 16, and f(16) also equals 16.
(C) If f(x) = (x+14)/2, then f(2) = 16/2 = 8. f(8) = 22/2 = 11. This looks like our answer.
(D) If f(x) = (2r2)x, then f(2) = 4r2. f(4r2) = (2r2)(4r2) = 16.
(E) If f(x) = x^2, then f(x) = 4. f(4) = 16.
Choice (C) is correct.