Find the domain of the following functions:
`(1)/(sqrt(4-x))`

Answer

To find the domain of the function \( f(x) = \frac{1}{\sqrt{4 - x}} \), we need to determine the values of \( x \) for which this 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 \( \sqrt{4 - x} \). 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 to ensure that:
\[ 4 - x > 0 \]
This inequality ensures that the square root is positive.

3. **Solve the inequality**:
\[ 4 > x \quad \text{or} \quad x < 4 \]

4. **Consider the case when the denominator is zero**: We also need to ensure that the denominator does not equal zero:
\[ \sqrt{4 - x} \neq 0 \]
This occurs when:
\[ 4 - x \neq 0 \quad \Rightarrow \quad x \neq 4 \]

5. **Combine the results**: From the inequality \( x < 4 \) and the condition \( x \neq 4 \), we conclude that the function is defined for all \( x \) less than 4, but not equal to 4.

6. **Write the domain in interval notation**: The domain of the function can be expressed in interval notation as:
\[ (-\infty, 4) \]

### Final Answer:
The domain of the function \( f(x) = \frac{1}{\sqrt{4 - x}} \) is \( (-\infty, 4) \).