State the Domain of h(x) / f(x) using interval notation

Question

Given functions h(x) = 1 / sqrt(x) and f(x) = x^2 - 4, state the domain of the following using interval notation: h(x) / f(x)

Answer 1

The domain of √x is x > 0 but this is 1/√x so that portion of the function requires the domain be x > 0.

The denominator (x² - 4) also affects the domain since we cannot divide by zero so that portion of the function requires the domain be to be not equal to ±2. Since -2 is already restricted by the 1/√x we can "ignore" that.

So the combination of the two restrictions results in a domain of (0, 2) U (2, ∞)