The domain of f(x) = `(1)/(sqrt(x - 3))` is :

Options

A. `(-oo, 3)`
B. `(3,oo)`
C. `[3,oo)`
D. None of these

Answer

To find the domain of the function \( f(x) = \frac{1}{\sqrt{x - 3}} \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the expression under the square root**: The function has a square root in the denominator, which is \( \sqrt{x - 3} \). For the function to be defined, the expression inside the square root must be positive (since we cannot take the square root of a negative number) and cannot be zero (since it is in the denominator).

2. **Set up the inequality**: We need \( x - 3 > 0 \) to ensure the square root is defined and positive. This leads us to the inequality:
\[ x - 3 > 0 \]

3. **Solve the inequality**: Adding 3 to both sides gives:
\[ x > 3 \]

4. **Determine the domain**: The values of \( x \) that satisfy this inequality are all real numbers greater than 3. In interval notation, this is expressed as:
\[ (3, \infty) \]

5. **Conclusion**: Therefore, the domain of the function \( f(x) = \frac{1}{\sqrt{x - 3}} \) is \( (3, \infty) \).

### Final Answer:
The domain of \( f(x) = \frac{1}{\sqrt{x - 3}} \) is \( (3, \infty) \).

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