Final answer:
The function f(x) = 6x/(x² - 9) is equal to zero at x = 0.
Step-by-step explanation:
To determine where the function f(x) = 6x/(x² - 9) is equal to zero, we set the function equal to zero and solve for x:
6x/(x² - 9) = 0
To solve this equation, we first factor the denominator:
x² - 9 = (x - 3)(x + 3)
Now we have:
6x/[(x - 3)(x + 3)] = 0
Since the numerator is 6x, the function is equal to zero when x = 0. However, the denominator cannot equal zero. So the function is equal to zero at x = 0.