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. $[2,3]$
• D. $[1,2)$

Answer 1

Answer: (B)

$[2,3)$

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

Now, $f\left(x\right)$ will be defined if

$|x-3|\le 1$

or, $-1\le x-3\le 1$

or, $2\le x\le 4$......(1),

and $9-x^2>0$

or, $x^2<9$

or, $-3<x<3$.....(2).

So $f\left(x\right)$ will be defined in the common portion of (1) and (2).

And the common protion is $2\le x<3$ or, $x\in [2,3)$.