Find the domain and range of `f(x)="sin"^(-1)(x-[x]),` where [.] represents the greatest integer function.

Explanation

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

### Step 1: Understand the Greatest Integer Function
The greatest integer function \([x]\) gives the largest integer less than or equal to \(x\). Therefore, we can express \(x\) as:
\[ x = [x] + \{x\} \]
where \(\{x\} = x - [x]\) is the fractional part of \(x\).
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