Q90 / 225 · JEE Main 2002 · Mathematics

The domain of $\sin ^{-1}\left[\log _3(x / 3)\right]$ is

  • Correct answer
    A
    [1, 9]
  • B
    [-1,9]
  • C
    [-9, 1]
  • D
    [-9, -1]

Solution

$f(x)=\sin ^{-1}\left(\log _3\left(\frac{x}{3}\right)\right)$ exists if $-1 \leq \log _3\left(\frac{x}{3}\right) \leq 1 \Leftrightarrow 3^{-1} \leq \frac{x}{3} \leq 3^1 \Leftrightarrow 1 \leq x \leq 9$ or $x \in[1,9]$

Hence, the correct answer is option: 'A'.

Relevant Questions