Question

Find the open intervals on which f(x) = (x^2) / (x^2 - 9).

Answer 1

The open intervals on which f(x) = (x^2) / (x^2 - 9) is defined are (-∞, -3) U (-3, 3) U (3, ∞).

Step-by-step explanation:

To find the open intervals on which f(x) = (x^2) / (x^2 - 9) is defined, we need to consider the values of x that would make the denominator equal to zero. The denominator, x^2 - 9, is equal to zero when x = 3 or x = -3. These are the points where the function is undefined. So, the open intervals on which f(x) is defined are (-∞, -3) U (-3, 3) U (3, ∞).