Explanation:

- Start with \( x = 3 - 2\sqrt{2} \).

- To simplify, check if \(\sqrt{x}\) has a simpler form. Assume \( \sqrt{x} = \sqrt{a} - \sqrt{b} \) for simplicity.

- Comparing, we find that \( x = 3 - 2\sqrt{2} = (\sqrt{a} - \sqrt{b})^2 = a + b - 2\sqrt{ab} \).

- So, \( a + b = 3 \) and \( 2\sqrt{ab} = 2\sqrt{2} \), which gives \( ab = 2 \).

- Solve: \( a = 2 \) and \( b = 1 \) (satisfying both conditions).

- Thus, \( \sqrt{x} = \sqrt{2} - 1 \).

- Calculate \(\frac{1}{\sqrt{x}} = \frac{1}{\sqrt{2} - 1} = \sqrt{2} + 1\) by rationalizing.

- Therefore, \(\sqrt{x} + \frac{1}{\sqrt{x}} = (\sqrt{2} - 1) + (\sqrt{2} + 1) = 2\sqrt{2}\).

- Correct Answer: Option 4: \( 2\sqrt{2} \)