Find the domain and range of the function `f(x) = sin^(-1)((1+e^(x))^(-1))`.

Explanation

To find the domain and range of the function \( f(x) = \sin^{-1}((1 + e^x)^{-1}) \), we will follow these steps:

### Step 1: Determine the Domain

1. **Identify the inner function**: The function inside the sine inverse is \( (1 + e^x)^{-1} \).
2. **Find the conditions for the sine inverse**: The sine inverse function, \( \sin^{-1}(y) \), is defined for \( y \) in the interval \([-1, 1]\).
3. **Analyze \( (1 + e^x)^{-1} \)**:
- Since \( e^x > 0 \) for all real \( x \), we have \( 1 + e^x > 1 \).
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