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Question

If xϵ[1,1],then range of tan1(x) is

A
[3π4,7π4]
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B
[3π4,5π4]
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C
[π,0]
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D
[π4,π4]
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Solution

The correct option is D [π4,π4]
This can be visualized and solved with the help of graphs. we know the graph of y=tan1(x) is

Now tan1(x) is simply flipping of this curve with respect to the y - axis.
y=tan1(x)

Now all we have to do it to see the y - coordinates of the point x = -1, and x = 1. Since the function is strictly decreasing we can say all points in between these two will constitute the range of the function.
tan1((1))=π4
tan1((1))=π4
Required range=[π4,π4]

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