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Determine where the function f(x) = 6x/(x² - 9) is continuous.

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Final answer:

The function f(x) = 6x/(x² - 9) is continuous everywhere except for x = 3 and x = -3.

Step-by-step explanation:

The function f(x) = 6x/(x² - 9) is continuous everywhere except at the values of x where the denominator is equal to zero. Therefore, to find where the function is continuous, we need to find the values of x that make the denominator zero. The denominator, x² - 9, is equal to zero when x = 3 and x = -3. So the function is not continuous at x = 3 and x = -3. For all other values of x, the function is continuous.

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