Inverse Trigonometric Functions Question 170

Question: The range of $ {{\tan }^{-1}} $ x is

[DCE 2002]

Options:

A) $ ( \pi ,\frac{\pi }{2} ) $

B) $ ( -\frac{\pi }{2},\frac{\pi }{2} ) $

C) $ (-\pi ,\pi ) $

D) $ (0,\pi ) $

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Answer:

Correct Answer: B

Solution:

f(x)= $ {{\tan }^{-1}} $ x

[Solution: $\frac{−π}{2}<f(x)<\frac{π}{2}$

IntervalNotation:$(\frac{−π}{2},\frac{π}{2})$]