Find the domain of `sin^(-1)(2x^(2)+1)`

Explanation

To find the domain of the function \( \sin^{-1}(2x^2 + 1) \), we need to determine the values of \( x \) for which the expression inside the sine inverse function is valid.

### Step-by-step Solution:

1. **Understand the Domain of \( \sin^{-1}(x) \)**:
The function \( \sin^{-1}(x) \) is defined for \( x \) in the interval \([-1, 1]\). This means that for \( \sin^{-1}(2x^2 + 1) \) to be defined, the expression \( 2x^2 + 1 \) must lie within this interval.

2. **Set Up the Inequality**:
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