Question

The domain of the function $f\left(x\right)={\sin }^{-1}\left(\frac{x+5}{2}\right)$ is :

• A. $[-1.1]$
• B. $[2,3]$
• C. $[3,7]$
• D. $[-7,-3]$
• E. $(-\infty ,\infty )$

Answer 1

The correct option is D $[-7,-3]$

Given, $f\left(x\right)={\sin }^{-1}\left(\frac{x+5}{2}\right)$
[ $\because$ Domain of $si{n}^{-1}x$ is $ϵ[-1,1]$ ]
For $f\left(x\right)$ to be defined
$-1\le \frac{x+5}{2}\le 1$
$\Rightarrow -2\le x+5\le 2$
$\Rightarrow -2-5\le x\le 2-5$
$\Rightarrow -7\le x\le -3$
Thus $xϵ[-7,-3]$