Let $f:\left(0,\infty \right)\vec{R}$ be given by $f\left(x\right)={\int }_{\frac{1}{x}}^x\frac{e^{-\left(t+\frac{1}{t}\right)}dt}{t},$ then (a)$f\left(x\right)$ is monotonically increasing on $\left[1,\infty \right)$(b)$f\left(x\right)$ is monotonically decreasing on $\left(0,1\right)$(c)$f\left(2^x\right)$ is an odd function of $x$ on $R$

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