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 $$ \frac{g(x)}{p(x)}: \square $$

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To determine the domain of the function $$\frac{g(x)}{p(x)}$$, where $$g(x) = \frac{1}{\sqrt{x}}$$ and $$p(x) = x^2 - 4$$, follow these steps:

1. **Ensure the Denominator is Not Zero:**
   - $$p(x) = x^2 - 4$$ should not be zero.
   - Solve $$x^2 - 4 \neq 0$$:
     $$
     x^2 \neq 4 \implies x \neq \pm 2
     $$
   
2. **Ensure the Inside of the Square Root is Positive:**
   - $$g(x) = \frac{1}{\sqrt{x}}$$ requires $$\sqrt{x}$$ to be defined and not zero.
   - Thus, $$x > 0$$.

3. **Combine the Conditions:**
   - From step 1, $$x \neq 2$$ (since $$x > 0$$ already excludes $$x = -2$$).
   - From step 2, $$x > 0$$.

Putting it all together, the domain consists of all positive real numbers except $$x = 2$$.

**Domain in Interval Notation:**
$$
(0, 2) \cup (2, \infty)
$$

**Final Answer:**
$$(0,\,2)\ \cup\ (2,\ \infty)$$
The domain of $$\frac{g(x)}{p(x)}$$ is all positive real numbers except $$x = 2$$, which can be written as $$(0,\,2)\ \cup\ (2,\ \infty)$$.

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

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