Question

Number of integer(s) for which the function
$f\left(x\right)={\sin }^{-1}\left({\log }_2\left(\frac{x}{3}\right)\right)$ is defined is

• A. 5.0
• B. 05
• C. 5.00
• D. 5

Answer 1

Answer: (A), (B), (C), (D)

$y={\sin }^{-1}\left({\log }_2\left(\frac{x}{3}\right)\right)$
$y={\sin }^{-1}\theta$ is defined for $\theta \in [-1,1]$
$\Rightarrow -1\le {\log }_2\left(\frac{x}{3}\right)\le 1$
$\Rightarrow \frac{1}{2}\le \frac{x}{3}\le 2$
$\Rightarrow \frac{3}{2}\le x\le 6$
Integers are $2,3,4,5,6\Rightarrow 5$ integers