If `f (x) =(1)/(sqrt(5x -7)),` then dom (f) =

Options

A. `R - {(7)/(5)}`
B. `[(7)/(5), oo)`
C. `[(5)/(7), oo)`
D. `((7)/(5), oo)`

Answer

To find the domain of the function \( f(x) = \frac{1}{\sqrt{5x - 7}} \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the condition for the square root**:
The expression inside the square root, \( 5x - 7 \), must be greater than zero because the square root of a negative number is not defined in the real number system. Therefore, we set up the inequality:
\[ 5x - 7 > 0 \]

2. **Solve the inequality**:
To solve for \( x \), we add 7 to both sides:
\[ 5x > 7 \]
Next, we divide both sides by 5:
\[ x > \frac{7}{5} \]

3. **Determine the domain**:
The solution \( x > \frac{7}{5} \) indicates that the function is defined for all \( x \) greater than \( \frac{7}{5} \). In interval notation, this can be expressed as:
\[ \text{dom}(f) = \left( \frac{7}{5}, \infty \right) \]

### Final Answer:
The domain of the function \( f(x) = \frac{1}{\sqrt{5x - 7}} \) is:
\[ \text{dom}(f) = \left( \frac{7}{5}, \infty \right) \]