Q78 / 200 · Manipal (MET) 2011 · Mathematics

The domain and range of $f(x)=\sin ^{-1}[x]$ are

  • A
    $[0,2),\left\{-\frac{\pi}{2}, \frac{\pi}{2}\right\}$
  • Correct answer
    B
    $[-1,2),\left\{-\frac{\pi}{2}, 0, \frac{\pi}{2}\right\}$
  • C
    $[-1,2),\left\{-\pi, \frac{-\pi}{2}, 0, \frac{\pi}{2}, \pi\right\}$
  • D
    None of the above

Solution

$f(x)=\sin ^{-1}[x]$ is defined, if $-1 \leq[x] \leq 1$ $\Rightarrow \quad[x]=\{-1,0,1\}$ $\therefore \quad x \in[-1,2)$ $\therefore$ Range is $\left\{\sin ^{-1}(-1), \sin ^{-1} 0, \sin ^{-1} 1\right\}$ $=\left\{-\frac{\pi}{2}, 0, \frac{\pi}{2}\right\}$

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

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