Question

If $y={\sin }^{-1}\left[2x\right]$, where $\left[x\right]$ is the greatest integer function, then $x$ belongs to

• A. $[\frac{1}{2},\frac{1}{2}]$
• B. $[-\frac{1}{2},1]$
• C. $[-\frac{1}{2},0]$
• D. $[-\frac{1}{2},1)$

Answer 1

The correct option is D $[-\frac{1}{2},1)$

Given

$y={\sin }^{-1}\left[2x\right]$

The range of ${\sin }^{-1}x$ is $[-1,1]$

$⟹-1\le \left[2x\right]\le 1$

$⟹-1\le 2x<2$

$⟹-\frac{1}{2}\le x<1$

$⟹x\in [-\frac{1}{2},1)$