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)

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