Final answer:
The domain of the function f(x)*g(x) is the set of all real numbers except for x ≠ -4 and x ≠ 3, because these values make the denominators of f(x) and g(x) zero and division by zero is undefined.
Step-by-step explanation:
In mathematics, the domain of a function is the set of all possible inputs for the function. For the multiplication of two functions f(x) and g(x), the domain is the set of all real numbers except where the individual functions' denominators equal zero, as division by zero is undefined.
In the given question, for f(x)=(-x-5)/(x+4), the denominator becomes zero when x = -4. Thus, x ≠ -4. Similarly, for g(x)=(x-3)/(-2x-6), by factorizing the denominator we get -2(x-3), and it becomes zero when x = 3. Hence, x ≠ 3. Combining these,
the domain of the function f(x)*g(x) is the set of all real numbers except x ≠ -4 and x ≠ 3.
Learn more about Domain of Functions