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 ensure that the argument of the inverse sine function lies within the valid range for the sine inverse function. The sine inverse function, \( \sin^{-1}(y) \), is defined for \( y \) in the interval \([-1, 1]\).

### Step-by-Step Solution:

1. **Identify the Argument**:
The argument of the function is \( 2x - 3 \).

2. **Set Up the Inequality**:
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