Question

Find g/f and its domain when g(x) = x² - 4x - 5 and f(x) = 4 - 3x.

A. g/f = x² - 4x - 5 / 4 - 3x; domain x ≠ 4/3.
B. g/f = 4 - 3x / x² - 4x - 5; domain x ≠ 4/3.
C. g/f = 4 - 3x / x² - 4x - 5; domain x ≠ -5, 1.
D. g/f = 4 - 3x / x² - 4x - 5; domain x ≠ 5, -1.

Answer 1

The quotient g/f is (x² - 4x - 5) / (4 - 3x) and the domain is all real numbers except for x ≠ 4/3, making option A the correct answer.

Step-by-step explanation:

The question asks us to find the quotient g/f where g(x) = x² - 4x - 5 and f(x) = 4 - 3x and to determine its domain. First, we form the quotient:

g/f = (x² - 4x - 5) / (4 - 3x)

To find the domain, we need to identify where the denominator is not zero since division by zero is undefined. Setting the denominator equal to zero gives us 4 - 3x = 0, which can be solved to find that x = 4/3. This means the function is undefined at x = 4/3.

Therefore, the correct option is A. g/f is equal to (x² - 4x - 5) / (4 - 3x) and the domain is all real numbers except x ≠ 4/3.