If the function g: (-∞, ∞) arrow (-(π)/2, (π)/2 ) is given by g(u) = 2tan^-1(e^u) - (π)/2. Then, g is

even and is strictly increasing in (0, ∞)

odd and is strictly decreasing in (-∞, ∞)

odd and is strictly increasing in (-∞, ∞)

neither even nor odd but is strictly increasing in (-∞, ∞)

If the function g: (-∞, ∞) arrow (-(π)/2, (π)/2 ) is given… — JEE Main 2008 Mathematics PYQ

AIEEE 2008

If the function

g: (-\infty, \infty) \rightarrow \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

is given by

g(u) = 2\tan^{-1}(e^u) - \frac{\pi}{2}

. Then,

g

Show answer

Correct option: A

[AIEEE 2008]

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