Question

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

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

Hint:

Always intersect all domain conditions.

Answer 1

The Correct Option is A

Step 1: For \(\sin^{-1}(x-3)\): \[ -1\le x-3\le1 \Rightarrow 2\le x\le4. \]
Step 2: For denominator: \[ 9-x^2 > 0 \Rightarrow -3 < x < 3. \]
Step 3: Intersection: \[ 2\le x < 3 \Rightarrow [1,2]. \]