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Limits Continuity and Differentiability question

2008 · Shift 2 · Q34

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2008 · Shift 2 · Q34

Limits Continuity and Differentiability question

2008 · Shift 2 · Q34

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMCQ+3 / −1

Let the function

g:\left( { - \infty ,\infty } \right) \to \left( { - {\pi \over 2},{\pi \over 2}} \right)

be given by

g\left( u \right) = 2{\tan ^{ - 1}}\left( {{e^u}} \right) - {\pi \over 2}.

Then,

g

is

A
even and is strictly increasing in $\left( {0,\infty } \right)$
B
odd and is strictly decreasing in $\left( { - \infty ,\infty } \right)$
C
odd and is strictly increasing in $\left( { - \infty ,\infty } \right)$
D
neither even nor odd, but is strictly increasing in $\left( { - \infty ,\infty } \right)$

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