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 $$ \frac{g(x)}{p(x)}:(0,2) \cup(2, \infty) $$ Domain of $$ g(p(x)):(-\infty,-2) \cup(2, \infty) $$ Domain of $$ p(g(x)): \square $$

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To determine the domain of $$ p(g(x)) $$, let's break down the functions and their compositions.

### Given Functions:
- $$ g(x) = \frac{1}{\sqrt{x}} $$
- $$ p(x) = x^2 - 4 $$

### Composition $$ p(g(x)) $$:
$$ p(g(x)) = p\left(\frac{1}{\sqrt{x}}\right) = \left(\frac{1}{\sqrt{x}}\right)^2 - 4 = \frac{1}{x} - 4 $$

### Determining the Domain:
1. **Inner Function $$ g(x) $$:**
   - $$ \sqrt{x} $$ is defined for $$ x > 0 $$.
   - The expression $$ \frac{1}{\sqrt{x}} $$ requires $$ x > 0 $$ to avoid division by zero.

2. **Composite Function $$ p(g(x)) $$:**
   - Since $$ p(x) $$ is a polynomial, it's defined for all real numbers.
   - Therefore, the domain of $$ p(g(x)) $$ is solely determined by the domain of $$ g(x) $$.

### Final Domain:
$$ \text{Domain of } p(g(x)): \ (0, \infty) $$

**Interval Notation:** $$ (0, \infty) $$
The domain of $$ p(g(x)) $$ is $$ (0, \infty) $$.

Given functions and , state the domains of the following functions using
interval notation.
Domain of
Domain of
Domain of

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