A) \[[0,\,\,2),\,\,\left\{ -\frac{\pi }{2},\,\,\frac{\pi }{2} \right\}\]
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
Correct Answer: B
Solution :
\[f(x)={{\sin }^{-1}}[x]\]is defined, if\[-1\le [x]\le 1\] \[\Rightarrow \] \[[x]=\{-1,\,\,0,\,\,1\}\] \[\therefore \] \[x\in [-1,\,\,2)\] \[\therefore \]Range is\[\{{{\sin }^{-1}}(-1),\,\,{{\sin }^{-1}}0,\,\,{{\sin }^{-1}}1)\] \[=\left\{ -\frac{\pi }{2},\,\,0,\,\,\frac{\pi }{2} \right\}\]
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