Inverse Trigonometric Functions

If $A=\left\{x \in R / \sin ^{-1}\left(\sqrt{x^2+x+1}\right) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\right\}$ and $B=\left\{y \in R / y=\sin ^{-1}\left(\sqrt{x^2+x+1}\right), x \in A\right\}$, then