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

Question

Let the function g : ( − ∞ , ∞ ) → ( − 2 π ​ , 2 π ​ ) be given by g ( u ) = 2 tan − 1 ( e u ) − 2 π ​ . Then g is

TestHub · Accepted Answer

g ( − u ) = 2 tan − 1 e − u − 2 π ​ = 2 cot − 1 e u − 2 π ​ = 2 ( 2 π ​ − tan − 1 e u ) − 2 π ​ = − ( 2 tan − 1 e u − 2 π ​ ) = − g ( u ) g ′ ( u ) = 2 ⋅ 1 + e 2 u 1 ​ ⋅ e u > 0 . So, g ( u ) is odd and strictly increasing.

Mathematics - Application of Derivative Question with Solution | TestHub

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