Find the domain and range of `f(x)=sin^(-1)[x]w h e re[ ]` represents the greatest function).

Explanation

To find the domain and range of the function \( f(x) = \sin^{-1}[\lfloor x \rfloor] \), where \([\lfloor x \rfloor]\) represents the greatest integer function (also known as the floor function), we will follow these steps:

### Step 1: Determine the Domain
The function \( \sin^{-1}(x) \) is defined only for \( x \) in the interval \([-1, 1]\). Therefore, we need to find the values of \( x \) for which \(\lfloor x \rfloor\) lies within this interval.

1. **Identify the values of \(\lfloor x \rfloor\)**:
- The greatest integer function \(\lfloor x \rfloor\) can take integer values. For \( f(x) \) to be defined, we require:
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