JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

Let

f: R \rightarrow R, f(x)=\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)+\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)

.
If the value of

f(\sqrt{3})+f(-\ln 2)+f(1)+f(\ln 3)

is equal to

k \pi(k \in W)

, then find the value of

k

View answer and explanation

Correct option: A

Option A (2) is correct because it's derived from using Leibniz's rule to differentiate the integral equation and then solving for k(1).

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S=\left\{x: f(x)=f^{-1}(x)\right\}