Final answer:
The domain of the function f(x) = (x-2)/(x²-4x-12) is all real numbers except x = 6 and x = -2.
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. To find the domain of the given function f(x) = (x-2)/(x²-4x-12), we need to determine the values of x that would make the denominator equal to zero, since division by zero is undefined.
To find the values of x that make the denominator zero, we can factor the quadratic expression x²-4x-12. Factoring it, we get: (x-6)(x+2). Setting each factor equal to zero, we find x = 6 and x = -2.
Therefore, the domain of the function consists of all real numbers except x = 6 and x = -2. In interval notation, the domain can be written as (-∞, -2) ∪ (-2, 6) ∪ (6, ∞).
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