1. **State the problem:** Find the domain of the function $$f(x) = \frac{\sqrt{x - 2}}{x^2 - 4}$$. 2. **Recall domain rules:** - The expression inside the square root must be $\geq 0$ because the square root of a negative number is not real. - The denominator cannot be zero because division by zero is undefined. 3. **Apply the square root domain condition:** $$x - 2 \geq 0 \implies x \geq 2$$ 4. **Apply the denominator restriction:** $$x^2 - 4 \neq 0 \implies (x - 2)(x + 2) \neq 0 \implies x \neq 2 \text{ and } x \neq -2$$ 5. **Combine conditions:** - From step 3, $x \geq 2$ - From step 4, $x \neq 2$ So the domain is $$x > 2$$. 6. **Final answer:** The domain of $$f(x)$$ is $$\boxed{(2, \infty)}$$ which corresponds to option c.