The domain of the function f(x) = 3/(x²-6) is all real numbers except ±√6.
The domain of a function is the set of all possible input values for which the function is defined. In this case, we have the function f(x) = 3/(x²-6). We need to determine the values of x that make the denominator of the fraction non-zero.
The denominator x²-6 cannot equal zero, so we solve the equation x²-6 = 0.
By taking the square root of both sides and simplifying, we find that x = ±√6. Therefore, the domain of the function f(x) is all real numbers except ±√6.
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