The domain of the function `f(x)=(1)/(sqrtx)` is :

Options

A. `-oo lt x ltoo`
B. `0ltxltoo`
C. `R-{0}`
D. `0lexltoo`

Answer

To find the domain of the function \( f(x) = \frac{1}{\sqrt{x}} \), we need to determine the values of \( x \) for which this function is defined.

### Step-by-Step Solution:

1. **Identify the function**: The function given is \( f(x) = \frac{1}{\sqrt{x}} \).

2. **Determine the conditions for the square root**: The expression \( \sqrt{x} \) is defined only for \( x \geq 0 \). However, since it is in the denominator, we need to ensure that \( \sqrt{x} \) is not equal to zero (to avoid division by zero).

3. **Set up the inequality**: Therefore, we need:
\[ x > 0 \]
This means \( x \) must be greater than zero.

4. **Express the domain**: The domain of the function can be expressed in interval notation. Since \( x \) can take any value greater than 0, the domain is:
\[ (0, \infty) \]

5. **Conclusion**: The domain of the function \( f(x) = \frac{1}{\sqrt{x}} \) is \( (0, \infty) \).

### Final Answer:
The domain of the function \( f(x) = \frac{1}{\sqrt{x}} \) is \( (0, \infty) \).

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