Question

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

• A. [-1,1]
• B. [2, 3]
• C. [3, 7]
• D. [-7, -3]
• E. $(\infty ,\infty )$

Answer 1

Answer: (D)

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