Assertion (A): The range of the function f ( x )=2 sin^-1 x +(3 π)/2, where x ∈[-1,1], is [(π)/2, (5 π)/2]. Reason ( R ): The range of the principal…

Assertion (A) : The range of the function $\displaystyle \mathrm{f}(\mathrm{x})=2 \sin ^{-1} \mathrm{x}+\frac{3 \pi}{2}$, where $\displaystyle \mathrm{x} \in[-1,1]$, is $\displaystyle \left[\frac{\pi}{2}, \frac{5 \pi}{2}\right]$. Reason ( $\displaystyle R$ ) : The range of the principal value branch of $\displaystyle \sin ^{-1}(\mathrm{x})$ is $\displaystyle [0, \pi]$.