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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
The domain of $\sin ^{-1}\left[\log \left(\frac{x}{3}\right)\right]$ is
  • ✓
    [1,9]
  • B
    (-1,9)
  • C
    [-9,1]
  • D
    [-9,-1]
✓

Answer

Correct option: A.
[1,9]
(A)
$y=\sin ^{-1}\left[\log _3\left(\frac{x}{3}\right)\right]$
$\therefore \quad-1 \leq \log _3\left(\frac{x}{3}\right) \leq 1$
$\therefore \quad \frac{1}{3} \leq \frac{x}{3} \leq 3$
$\therefore \quad 1 \leq x \leq 9$
$\therefore \quad x \in[1,9]$

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