Let y=f(x) represent a parabola with focus (-1/2, 0) and directrix y=-1/2. Then S={x ∈ R: tan^-1(√(f(x)))+ sin^-1(√(f(x)+1))=(π)/2}:

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