Given functions \( g(x)=\frac{1}{\sqrt{x}} \) and \( p(x)=x^{2}-4 \), state the domains of the following functions using interval notation. Domain of \( \frac{g(x)}{p(x)}: \square \)

To determine the domain of \( \frac{g(x)}{p(x)} \), we must identify where both \( g(x) \) and \( p(x) \) are defined. For \( g(x) = \frac{1}{\sqrt{x}} \), this function is defined for \( x > 0 \) because the square root cannot be negative or zero. Therefore, the domain of \( g(x) \) is \( (0, \infty) \). For \( p(x) = x^2 - 4 \), this quadratic expression equals zero at \( x = 2 \) and \( x = -2 \), meaning \( p(x) \) is defined for all real numbers except those points. The domain of \( p(x) \) is \( (-\infty, -2) \cup (-2, 2) \cup (2, \infty) \). To find the domain of \( \frac{g(x)}{p(x)} \), we need the intersecting values where both functions are defined, excluding places where \( p(x) = 0 \). Thus the domain of \( \frac{g(x)}{p(x)} \) is: Domain of \( \frac{g(x)}{p(x)}: (0, 2) \cup (2, \infty) \)