Let the function g:(- , ) (- 2 , 2 ) be given by g(u)=2 ^ -1 (e^ u )- 2 Then, g is
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
Let the function \(g:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\) be given by \(g(u)=2 \tan ^{-1}\left(e^{u}\right)-\frac{\pi}{2}\) 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
(– ∞, ∞)
Answer
(D) neither even nor odd, but is strictly increasing in (– ∞ , ∞ )
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