A) R and R
B) \[\left[ 0,\frac{\pi }{2} \right]\] and [0,1]
C) \[\left[ \frac{-\pi }{2},\frac{\pi }{2} \right]\] 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 \[f(x)=\sin x\] 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.
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