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 \( 2x^2 + 1 \) lies within the valid range of the inverse sine function. The domain of \( \sin^{-1}(x) \) is defined for \( x \) values in the interval \([-1, 1]\). Therefore, we need to solve the following inequalities:

1. \( -1 \leq 2x^2 + 1 \leq 1 \)

### Step 1: Solve the first inequality \( -1 \leq 2x^2 + 1 \)

Subtract 1 from both sides:

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