Question

Let f(x) = 3x - 6 and g(x) = x - 2. Find f/g and state its domain.

3; all real numbers except x = 2


–3; all real numbers except x = 3


1; all real numbers


3; all real numbers

Answer 1

Hello!

The function f/g means that that f(x) is written in the numerator and g(x) is written in the denominator because we are dividing the functions f(x) and g(x). (f/g = f(x)/g(x))

f(x)/g(x) is shown as: (3x - 6)/(x - 2).

The function shown above can be factored before we find the domain, since the greatest common factor of the numerator is 3.

f(x)/g(x) = 3(x - 2)/(x - 2)

f(x)/g(x) = 3

The function y = 3 is a horizontal line, so it has a domain of all real numbers.

Therefore, f/g is 3, and its domain is all real numbers, which is choice D.