Question

The domain of the function ${\sin }^{-1}2x$ is:

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

Answer 1

The correct option is D $\left[\frac{-1}{2},\frac{1}{2}\right]$

${\sin }^{-1}2x$

In ${\sin }^{-1}\theta$

$\theta \in [-1,1]$

$\Rightarrow 2x\in [-1,1]$

$\Rightarrow x\in [\frac{-1}{2},\frac{1}{2}]$