Find the domain of the function. f(x)=x-2/$$ \sqrt{x} $$

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.

Find the domain of the function. f(x) = \frac{x - 2}{\sqrt{x}}

Discover how to find the domain of the function f(x) = (x - 2) / sqrt(x) by analyzing square root restrictions and denominator constraints. Suitable for high school students, this explanation covers the key algebraic concepts of radicals and functions.

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