Final answer:
The product of the functions f(x) = 3x^2 and g(x) = 3/(x+9) is 9x^2/(x+9), and its domain is all real numbers except x = -9, since the function becomes undefined at this point.
Step-by-step explanation:
To calculate the product of two functions, (fg)(x), you simply multiply function f(x) by function g(x). Given that f(x) = 3x2 and g(x) = 3/(x+9), we have:
(fg)(x) = f(x) × g(x) = (3x2) × (3/(x+9))
Now, multiply the two expressions:
(fg)(x) = 9x2/(x+9)
The domain of the product function is all x-values for which both f(x) and g(x) are defined. For g(x) = 3/(x+9), the only restriction is that x ≠ -9 because division by zero is undefined. As there are no restrictions on f(x), the domain of (fg)(x) is (-∞, -9) ∪ (-9, +∞).