Find the domain of the function `f(x)=sin^(-1)(2x-3)` .

Explanation

To find the domain of the function \( f(x) = \sin^{-1}(2x - 3) \), we need to determine the values of \( x \) for which the expression \( 2x - 3 \) lies within the valid range of the inverse sine function.

### Step-by-Step Solution:

1. **Identify the Range of the Inverse Sine Function**:
The inverse sine function, \( \sin^{-1}(y) \), is defined for \( y \) in the interval \([-1, 1]\). Therefore, we need to ensure that:
\[
-1 \leq 2x - 3 \leq 1
...