Let f   : 0 ,   ∞ → R be given by f x =   ∫ 1 x x e - t + 1 t d t t , then

1. $f\left(x\right)$ is monotonically increasing on $\left[1, \infty \right)$
2. $f\left(x\right)$ is monotonically decreasing on (0, 1)
3. $f\left(x\right)+f\left(\frac{1}{x}\right)=0,$ for all $x \in \left(0, \infty \right)$
4. $f\left(2^x\right)$ is an odd function of $x$ on R

Solution

Asked in: JEE Advanced 2014 (Paper 1)

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