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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
The domain of the function $f (x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^2}}$ is
  • A
    [1,2)
  • ✓
    ( 2, 3)
  • C
    [1,2]
  • D
    [2, 3]
✓

Answer

Correct option: B.
( 2, 3)
(B)
To define $f (x), 9-x^2>0 \Rightarrow|x|<3$
$\Rightarrow-3< x< 3,$ ...(i)
and $-1 \leq(x-3) \leq 1$
$\Rightarrow 2 \leq x \leq 4$ ...(ii)
From (i) and (ii), $2 \leq x<3$ i.e., $[2,3)$.

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