A) R and R
B) \[[0,\pi ]\]and [0,1]
C) \[\left[ 0,\frac{\pi }{2} \right]\]and \[[-1,1]\]
D) \[\left[ \frac{-\pi }{2},\frac{\pi }{2} \right]\]and \[[-1,1]\]
Correct Answer: C
Solution :
Since,\[f:X\to Y,\]then\[f(x)=sin\text{ }x\] Now, take option (c). Domain\[=\left[ 0,\frac{\pi }{2} \right],\]Range\[=[-1,1]\] For every value of\[x,\]we get unique value of y. But the value of y in\[[-1,0)\]does not have any pre-image. \[\therefore \]Function is one-one but not onto.You need to login to perform this action.
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