Question

Determine the domain of (f/g)(x) when f(x) = -1/x and g(x) = sqrt(3x - 9).

A) x > 3
B) x < 3
C) x ≠ 3
D) x > 0

Answer 1

The domain of (f/g)(x), where f(x) = -1/x and g(x) = sqrt(3x - 9), is x < 3. The correct statement is option B) x < 3

Step-by-step explanation:

The domain of the function (f/g)(x) can be determined by finding the values of x for which the function is defined. In this case, we need to consider the restrictions on the domain of both f(x) = -1/x and g(x) = sqrt(3x - 9).

For f(x) = -1/x, the function is undefined when x = 0 since division by zero is not defined. Therefore, the domain of f(x) is all real numbers except x = 0.

For g(x) = sqrt(3x - 9), the function is undefined when the expression inside the square root becomes negative. So, we need to find the values of x for which 3x - 9 < 0. Solving this inequality, we get x < 3. Therefore, the domain of g(x) is x < 3.

To find the domain of (f/g)(x), we need to consider the intersection of the domains of f(x) and g(x). In this case, the domain of (f/g)(x) is x < 3, since x = 0 is excluded from the domain of f(x). The correct statement is option B) x < 3