Domain and Range of Basic Inverse Trigonometric Functions
If x ϵ[-1,1],...
Question
If xϵ[−1,1],thenrangeoftan−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 ∴Requiredrange=[−π4,π4]