The function given is:

$f(x) = \frac{x - 2}{\sqrt{x}}$

To find the domain of this function, we need to determine the set of values for $x$ that make the function well-defined. Two things must be true for this function to be valid:

1. The square root function $\sqrt{x}$: The expression inside the square root must be non-negative, i.e., $x \geq 0$. This is because the square root of a negative number is not a real number.

2. The denominator $\sqrt{x}$: The denominator must be non-zero, so $\sqrt{x} \neq 0$. This means that $x \neq 0$.

Combining these conditions:

• From the square root condition: $x \geq 0$
• From the denominator condition: $x \neq 0$

Therefore, the domain of the function is all positive real numbers, i.e., $x > 0$.

Domain:

$\boxed{(0, \infty)}$

Would you like more details or have any questions?

Here are some related questions:

1. How do you find the domain of more complex functions involving square roots?
2. What happens to the function's behavior as $x$ approaches 0?
3. How does the presence of a square root affect the domain compared to polynomials?
4. What is the range of the function $f(x) = \frac{x - 2}{\sqrt{x}}$?
5. Can you generalize the process for finding domains of functions with radicals and fractions?

Tip: Always remember to check for restrictions both from the denominator and the square root when finding domains.