Consider , defined as f(x)= ^ -1 ( _e x ( _e x)^2+1 ). The above function can be…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider f:(0,∞)→(−π2,π2)f:(0,\infty)\to\left(-\frac{\pi}{2},\frac{\pi}{2}\right), defined as f(x)=tan⁡−1(log⁡ex(log⁡ex)2+1).f(x)=\tan^{-1}\left(\frac{\log_e x}{(\log_e x)^2+1}\right). The above function can be classified as (1) Injective but not surjective (2) Surjective but not bijective (3) Neither injective nor surjective (4) Both injective and surjective

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