Let f(x) = 3x - 6 and g(x) = x - 2. Find f/g and its domain.
A. 3; all real numbers
B. 3; all real numbers except x = 2
C. -3; all real numbers except x = 3
D. 1; all real numbers
B ?
f/g = (3x-6)/(x-2) = 3
B is correct
Thank you
To find the function f/g, we need to divide f(x) by g(x).
First, let's write out the expression for f and g:
f(x) = 3x - 6
g(x) = x - 2
To find f/g, we divide f(x) by g(x). In other words, we substitute the expressions for f(x) and g(x) into the division:
f/g = (3x - 6)/(x - 2)
When dividing rational expressions, we look for any common factors that can be canceled out. In this case, we can see that (3x - 6) has a common factor of 3:
f/g = (3(x - 2))/(x - 2)
Now, we can cancel out the common factor of (x - 2):
f/g = 3
So, f/g is equal to 3.
Next, let's determine the domain of f/g. The domain refers to the set of all possible values for x for which the function is defined.
In the original problem, we had two functions, f(x) = 3x - 6 and g(x) = x - 2. The domain of f(x) is all real numbers because there are no restrictions.
However, for g(x) = x - 2, we cannot divide by zero. So, x - 2 should not equal zero.
Setting x - 2 = 0, we find that x cannot be equal to 2.
Therefore, the domain of f/g consists of all real numbers except for the value x = 2.
So, the correct answer is option B. f/g = 3; all real numbers except x = 2.