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]

Answer 1

Answer: (D)

[-7, -3]

Answer 2

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