Find the domain of the range of each of the following real functions:
`f(x)=(1)/(sqrt(2x-3))`

Explanation

To find the domain of the function \( f(x) = \frac{1}{\sqrt{2x - 3}} \), we need to ensure that the expression under the square root is positive, since the square root of a negative number is not defined in the real number system, and the denominator cannot be zero.

### Step-by-step Solution:

1. **Identify the condition for the square root**:
The expression under the square root must be greater than zero:
\[ 2x - 3 > 0 \]

2. **Solve the inequality**:
To solve the inequality, we can add 3 to both sides:
\[ 2x > 3 \]
Now, divide both sides by 2:
\[ x > \frac{3}{2} \]

3. **Determine the domain**:
The domain of the function is all values of \( x \) that satisfy the inequality \( x > \frac{3}{2} \). In interval notation, this is represented as:
\[ \text{Domain of } f = \left( \frac{3}{2}, \infty \right) \]