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Question

# If xϵ[−1,1],then range of tan−1(−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=tan−1(x) is Now tan−1(−x) is simply flipping of this curve with respect to the y - axis. ∴y=tan−1(−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. ∴tan−1(−(−1))=π4 tan−1(−(1))=−π4 ∴Required range=[−π4,π4]

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