If f(x)=2( ^-1(e^x)-/4), then f(x) is : Option 1: even and is strictly increasing in (0, ∞) Option 2: even and is strictly decreasing in (0, ∞) Option 3: odd and is strictly increasing in (-∞, ∞) Option 4: odd and is strictly decreasing in (-∞, ∞)

The answer is 'odd and is strictly increasing in (-∞, ∞)'. View full solution:

Calculus > Application of Derivatives

Medium

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If $f(x)=2\left(\tan ^{-1}\left(e^{x}\right)-\frac{\pi}{4}\right)$, then $f(x)$ is :

even and is strictly increasing in $(0, \infty)$

even and is strictly decreasing in $(0, \infty)$

odd and is strictly increasing in $(-\infty, \infty)$

odd and is strictly decreasing in $(-\infty, \infty)$

✅ Correct Option: 3

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