Question

The domain of the function $f\left(x\right)=\frac{{\sin }^{-1}(x-3)}{\sqrt{9-x^2}}$ is

• A. $[1,2]$
• B. $[2,3)$
• C. $(1,2)$
• D. $[2,3]$

Answer 1

Answer: (B)

$[2,3)$

$f\left(x\right)=\frac{{\sin }^{-1}(x-3)}{\sqrt{9-x^2}}$ is defined
if

$-1\le x-3\le 1\Rightarrow 2\le x\le 4$...................(1)

and
$\left(ii\right)9-x^2>0\Rightarrow -3<x<3$...................(2)

Taking common solution of (i) and (ii), we get $2\le x<3$
Therefore, domain is $[2,3)$.