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Q.

Let the function  g:(,)(π2,π2)  be given by g(u)=2tan1(eu)π2. Then, g  is

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a

even and is strictly increasing in  (0,)

b

odd and is strictly decreasing in   (,))

c

odd and is strictly increasing in  (,)

d

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

answer is C.

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Detailed Solution

g(u)=2tan1(eu)π2g(u)=2eu1+e2u>0

Hence g(u) is increasing function g(u)=g(u) 
Hence g(u)  is odd strictly increasing in (,)

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Let the function  g:(−∞,∞)→(−π2,π2)  be given by g(u)=2tan−1⁡(eu)−π2. Then, g  is