Question

The number of integral value(s) in the range of $f(x)=\sin \left({\cos }^{-1}\frac{x}{2}\right)+\sin \left({\tan }^{-1}\frac{\sqrt{4-x^2}}{x}\right)$ is (are)

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

$f(x)=\sin \left({\cos }^{-1}\frac{x}{2}\right)+\sin \left({\tan }^{-1}\frac{\sqrt{4-x^2}}{x}\right)=\{\begin{array}{ll}\sqrt{4-x^2};& 0<x\le 2\\ 0;& -2\le x<0\end{array}.$
$\therefore$ Range of $f$ is : $[0,2)$