Final answer:
To find (f/g)(6), we calculate f(6) = 13 and g(6) = 7, thus (f/g)(6) = 13 / 7. The values not in the domain of f/g are x = 5 and x = -1 as g(x) equals zero at these points and division by zero is undefined.
Step-by-step explanation:
To find (f/g)(6), we first evaluate f(6) and g(6) separately using the given functions f(x) = x + 7 and g(x) = (x - 5)(x + 1). Then we divide f(6) by g(6).
- f(6) = 6 + 7 = 13
- g(6) = (6 - 5)(6 + 1) = (1)(7) = 7
Now, (f/g)(6) = f(6) / g(6) = 13 / 7.
To find the values that are NOT in the domain of f/g, we need to determine where g(x) equals zero, since division by zero is undefined. The roots of g(x) are x = 5 and x = -1.
Therefore, the values that are NOT in the domain of f/g are x = 5 and x = -1.