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Question

f(x) = sin(x) defined on f: [π2,π2] [1,1] is -


A

One –One into

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B

One –one onto

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C

Many one into

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D

Many one onto

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Solution

The correct option is B

One –one onto


Here, the important thing we have to notice is that the domain is not R.

It is [π2,π2]. Now if we draw a graph of sinx for the domain [π2,π2].) . We’ll see that on the graph if we draw lines parallel to x –axis we’ll not find even a single line which would cut the graph more than once. So the function is one – one. Now we have to check whether the function is onto or not. The co- domain given is [1,1]. By drawing the graph itself we can see that the function is ranging from [1,1]. So the function is onto as well. Hence, f(x) = sin(x) defined on f: [π2,π2][1,1] is one - one onto.


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