For which intervals is f(x)=(sqrt(x^2-4)) / (x^2+x-6) continuous? What types of discontinuities are there in f?

Answer 1

Let find 1st domain of this function: x² - 4 ≥ 0 and x² + x - 6 ≠ 0; x ≤ - 2 or x ≥ 2; x ≠ - 3 and x ≠ 2.

So domain: (-∞, -3)U(-3, -2]U(2, ∞).

Now this function continuous on intervals (- ∞, -3), (-3,-2), (2, ∞).

At x = -3 and x = 2 we have infinite discontinuity