Final answer:
The domain of g is (7/4, [infinity]) and the range is (-[infinity], [infinity]).
Step-by-step explanation:
The correct answer is (c) Domain: (7/4, [infinity]) Range: (-[infinity], [infinity]).
To find the domain and range of g-1(x), we need to consider the restrictions on the original function g(x).
The given choices for g-1(x) are all of the form (x - 1)/(4x + 7), (x + 1)/(4x - 7), (x - 1)/(4x - 7), and (x + 1)/(4x + 7).
Out of these choices, only option (c) has a domain of (7/4, [infinity]) which means x can take any value greater than 7/4. And the range of option (c) is (-[infinity], [infinity]) which means y can take any real value.