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 $$ g(p(x)): $$

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To determine the domain of $$ g(p(x)) $$, let's break down the functions involved:

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

2. **Composition $$ g(p(x)) $$:**
   - $$ g(p(x)) = \frac{1}{\sqrt{p(x)}} = \frac{1}{\sqrt{x^2 - 4}} $$

3. **Determining the Domain:**
   - The expression inside the square root, $$ x^2 - 4 $$, must be **positive** because the square root of a non-positive number is undefined in the real number system.
   - So, we set up the inequality:
     $$
     x^2 - 4 > 0
     $$
   - Solving the inequality:
     $$
     x^2 > 4 \
     \Rightarrow x < -2 \quad \text{or} \quad x > 2
     $$
   
4. **Interval Notation:**
   - Combining the solutions, the domain of $$ g(p(x)) $$ is:
     $$
     (-\infty, -2) \cup (2, \infty)
     $$

**Final Answer:**

The domain of $$ g(p(x)) $$ is $$ (-\infty,\ -2) \cup (2,\ \infty) $$.
The domain of $$ g(p(x)) $$ is $$ (-\infty,\ -2) \cup (2,\ \infty) $$.

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

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