Final answer:
After examining each set of functions, none of the pairs I, II, III, or IV represents inverse functions. Therefore, none of the provided options A, B, C, or D are correct. This question might contain incorrect information or could be a trick question.
Step-by-step explanation:
To determine which sets of functions represent inverse functions, we need to check if one function undoes the operation of the other. Two functions, f(x) and g(x), are inverses if and only if applying g to the outcome of f (and vice versa) returns the original input x; formally written as g(f(x)) = x and f(g(x)) = x.
For I, applying g to f gives us g(f(x)) = g(2x + 3) = 3(2x + 3) + 2 ≠ x, and applying f to g gives us f(g(x)) = f(3x + 2) = 2(3x + 2) + 3 ≠ x. So, these do not represent inverse functions.
For II, g(x) = 1 is a constant function; it does not undo the operation of f(x) = 2x + 3, and vice versa, so these do not represent inverse functions.
For III, both f(x) and g(x) are constant functions with the same value; therefore, they cannot be inverses as they do not satisfy the basic definition of inverse functions where f(g(x)) = x and g(f(x)) = x.
For IV, f(x) and g(x) are again constant functions with different values; hence, they cannot be inverses as they do not return the original x after applying one to the outcome of the other.
None of the given pairs of functions are inverse functions of each other, so none of the options A, B, C, or D are correct. This question appears to contain incorrect information or may be a trick question.