Let \(y=f(x)\) represent a parabola with focus \(\left(-\frac{1}{2}, 0\right)\) and directrix \(y=-\frac{1}{2}\). Then \…

Let \(y=f(x)\) represent a parabola with focus \(\left(-\frac{1}{2}, 0\right)\) and directrix \(y=-\frac{1}{2}\). Then
\(S=\left\{x \in R: \tan ^{-1}\left(\sqrt{f(x)}+\sin ^{-1}(\sqrt{f(x)+1})\right)=\frac{\pi}{2}\right\}\) :

[JEE Main 2023, 31 Jan (Shift 1)]