Q 1115712660.     Let the function `g:(-oo,oo)->(-pi/2,pi/2)` be given by `g(u)=2tan^(-1) (e^u) -pi/2`. Then, `g` is :

JEE 2008
A

even and strictly increasing in `(0,oo)`

B

odd and strictly increasing in `(-oo,oo)`

C

odd and strictly decreasing in `(oo,oo)`

D

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

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