CUET CUET Mathematics 2024 - If f(x)=2( ^-1(e^x)-/4), then f(x) is : | PYQs + Solutions

CUET Mathematics 2024

Calculus

Application of Derivatives

Medium

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

Will be added.

Related questions:

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f(x)=x^{2}+b x+1

[1,2]

b

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f(x) = 2x^3 - 9x^2 + 12x - 5

x \in [0, 3]

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f(x)=\sin x+\frac{1}{2} \cos 2 x \text { in }\left[0, \frac{\pi}{2}\right]

f^{\prime}(x)=\cos x-\sin 2 x

x=\frac{\pi}{6}

x=\frac{\pi}{2}

2

\frac{3}{4}