Final answer:
The values that are not in the domain of the function f/g, where f(x)=x+7 and g(x)=(x-5)(x+1), are 5 and -1, because these values make g(x) equal to zero, leading to an undefined expression.
Step-by-step explanation:
The question requires us to find all values that are not in the domain of the function f/g where f(x) = x + 7 and g(x) = (x - 5)(x + 1). To find the domain of f/g, we need to determine where g(x) is not equal to zero since division by zero is undefined.
The zeroes of g(x) are the values of x that make g(x) equal to zero, which can be found by setting (x - 5)(x + 1) = 0. Thus, the values of x that make g(x) equal to zero are x = 5 and x = -1. These are the values that are not in the domain of f/g.
Therefore, the values that are NOT in the domain of f/g are 5 and -1. Any other real number can be used as an input for the function f/g.