The problem requires finding $(f + g)(x)$ where $f(x) = \sqrt{x - 2}$ and $g(x) = \sqrt{x}$. Here's the step-by-step solution:

1. By the definition of addition of functions,
   $(f + g)(x) = f(x) + g(x).$

2. Substituting the given expressions for $f(x)$ and $g(x)$: $(f + g)(x) = \sqrt{x - 2} + \sqrt{x}.$

3. Thus, the final expression for $(f + g)(x)$ is: $(f + g)(x) = \sqrt{x - 2} + \sqrt{x}.$

The correct answer is the fourth option:
$(f + g)(x) = \sqrt{x - 2} + \sqrt{x}.$

Let me know if you have further questions! Here are 5 related questions to expand your understanding:

1. How do we subtract functions instead of adding them?
2. What are the domain restrictions for the function $f(x) = \sqrt{x - 2}$?
3. Can $\sqrt{x - 2} + \sqrt{x}$ be simplified further?
4. What happens to $f(x) + g(x)$ if both functions include cube roots instead of square roots?
5. How does the graph of $f + g$ compare to the graphs of $f$ and $g$ individually?

Tip: When adding functions involving square roots, always check the domains of the individual functions to ensure they overlap.