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STD 12 - 1. relation and function — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 1. relation and function1 Mark
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
(b) To define $f(x)$,

$9 - {x^2} > 3 \Rightarrow - 3 < x < 3.....(i)$

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

From $(i)$ and $(ii)$, $2 \le x < 3$   $i.e.,\,\, [2, 3).$

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