Final answer:
Option B, f(x) = 2x + 13, correctly defines a bijection between the natural numbers and the set of all odd integers greater than 13, as it maps every natural number to a unique odd number greater than 13.
Step-by-step explanation:
To exhibit a bijection between ℕ (the set of natural numbers) and the set of all odd integers greater than 13, we need to find a function that pairs every element of ℕ with a unique odd integer greater than 13, and vice versa. A bijection means there is a one-to-one and onto relationship between the two sets.
Looking at the given options, we can eliminate options A and C because adding an even number (2x) to an odd number (13 or 11) would result in an even number, not an odd one. Option D, f(x) = 2x - 11, does not guarantee an odd result greater than 13. However, with option B, f(x) = 2x + 13, when x starts at 1, f(x) is 15, which is the smallest odd integer greater than 13. Furthermore, as x increases by 1, f(x) increases by 2, ensuring that all outputs are odd and greater than 13.
Therefore, option B defines a bijection as required. This function maps every natural number to a unique odd number greater than 13, without any overlaps or gaps.