The domain of a function f(x) is the set of all values of x for which the function is defined. Since we cannot divide by zero, the function f(x)=-1/(x+3)(x-3) will be undefined when (x+3)(x-3) = 0. There are two possiblities here: x = -3 and x = +3.

Therefore,

**The domain of f(x) = -1 / (x+3)(x-3) is all real numbers except -3 and 3.**

The value for any number divided by 0 is not defined. All the values that x can take for which f(x) has a real value is the domain of the function.

Here f(x) = -1/(x+3)(x-3) is not defined when x + 3 = 0 or x - 3 = 0

**This gives the domain as R - {-3 , 3}**

The domain of the function is represented by the interval that contains all the values of x that make the function to exist.

Since the expression of the function is a fraction, then the values of x that cancels the denominator must be rejected out from the domain.

We notice that x = -3 and x = 3 are cancelling out the denominator, therefore the maximum domain of the function is R-{-3 ; 3}.