Final answer:
To determine which of the given statements is correct, analyse the properties of functions f(x) and g(x). The correct answer is B) f and g have the same domain.
Step-by-step explanation:
In order to determine which of the given statements is correct, we need to analyse the properties of the functions f(x) and g(x). Let's start by looking at the domain of each function.
The domain of f(x) is all real numbers except for the values of x that make the denominator, x² - 2x - 3, equal to zero. We can factor the denominator as (x - 3)(x + 1), so the function is undefined for x = 3 and x = -1.
On the other hand, the domain of g(x) is all real numbers except for the values of x that make the denominator, 2x - 4, equal to zero. Solving for x, we find that the function is undefined for x = 2.
Since f(x) is undefined at x = 3 and g(x) is undefined at x = 2, statement A) is incorrect. However, statement B) is correct because both functions have the same domain for all other values of x. Therefore, the correct answer is B) f and g have the same domain.