A) I, the set of integers
B) N, the set of natural numbers
C) W, the set of whole numbers
D) \[\left\{ 1,2,3,4.... \right\}\]
Correct Answer: D
Solution :
[d] Since \[\{x\}\in [0,\,\,1),sin\{x\}\in (0,\,\,sin1)\] as \[f(x)\] is defined if \[\sin \{x\}\ne 0,\] i.e., \[\frac{1}{\sin \{x\}}\in \left( \frac{1}{\sin 1},\infty \right)\] Or \[\left[ \frac{1}{\sin \{x\}} \right]\in \{1,2,3...\}\] Note that \[1<\frac{\pi }{3}\] or \[\sin 1<\sin \frac{\pi }{3}=0.866\] or \[\frac{1}{\sin 1}>1.155.\]
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