A) injective
B) subjective
C) objective
D) None of these
Correct Answer: D
Solution :
We have, \[y=\sin \frac{x}{2}\] and \[0\le x\le \frac{\pi }{2}\] \[\Rightarrow \] \[0\le \frac{x}{2}\le \frac{\pi }{4}\] \[\Rightarrow \] \[0\le \sin \frac{x}{2}\] \[\le \frac{1}{\sqrt{2}}\] \[\Rightarrow \] \[\left( 0,\,\,\frac{1}{\sqrt{2}} \right)\subset [0,\,\,\infty )\] So, function is not surjective but function is injective as for any \[0\le x\le \frac{x}{2},\,\,\sin \frac{x}{2}\] gives unique image.
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