Final answer:
To find the domain of (f•g)(x), consider the domain restrictions of both functions f(x) and g(x). The domain of (f•g)(x) is all real numbers except x = -4 and x = 0.
Step-by-step explanation:
To find the domain of (f•g)(x), we need to consider the domain restrictions of both functions f(x) and g(x). The domain of f(x) = 1/(x+4) is all real numbers except x = -4, because dividing by zero is undefined. The domain of g(x) = -1/x is all real numbers except x = 0, because dividing by zero is also undefined.
Next, we need to determine the domain of the composition of f(x) and g(x). Since the composition (f•g)(x) involves multiplying the outputs of f(x) and g(x), we need to make sure that both functions are defined at the same values of x. Therefore, the domain of (f•g)(x) is all real numbers except x = -4 and x = 0.