JEE Main 202331 Jan, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002Let y=f(x)\mathrm{y}=f(x)y=f(x) represent a parabola with focus (−12,0)\left(-\frac{1}{2}, 0\right)(−21,0) and directrix y=−12y=-\frac{1}{2}y=−21. Then S={x∈R:tan−1(f(x))+sin−1(f(x)+1)=π2}S=\left\{x \in \mathbb{R}: \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}S={x∈R:tan−1(f(x))+sin−1(f(x)+1)=2π} :AOption A. is an empty setBOption B. contains exactly one elementCOption C. contains exactly two elementsDOption D. is an infinite setCheckSkip · show solution
