Final answer:
The domain of the function f(x) = \(\frac{1}{x^2-5x-6}\) is all real numbers except for x = 6 and x = -1. In interval notation, it is represented as \((-\infty, -1) \cup (-1, 6) \cup (6, \infty)\).
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the function f(x) = \(\frac{1}{x^2-5x-6}\), we must find the values of x for which the denominator is not zero since division by zero is undefined.
The denominator is a quadratic expression which can be factored as (x-6)(x+1). Setting the denominator equal to zero, we have x-6 = 0 or x+1 = 0, which gives us the solutions x = 6 and x = -1. These are the values we must exclude from the domain of the function.
Therefore, the domain is all real numbers except for x = 6 and x = -1. In interval notation, we write the domain as \((-\infty, -1) \cup (-1, 6) \cup (6, \infty)\).