Let f-0-R be given by f-x-x1-xe-t-1t-dtt- then

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Condition for Monotonically Decreasing Function

Question

Let $f : (0, \infty) \to R$ be given by $f (x) = \int_{1 / x}^{x} e^{(t + \frac{1}{t})} \frac{d t}{t}$ , then

f (x)

is monotonically increasing on

[1, \infty)

f (x)

is monotonically decreasing on (0, 1)

f (x) + f (\frac{1}{x}) = 0

, for all

x \in (0, \infty)

f (2^{x})

is an odd function of x on R

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Let f:(0,∞)→R be given by f(x)=∫x1/xe(t+1t)dtt, then

Let $f : (0, \infty) \to R$ be given by $f (x) = \int_{1 / x}^{x} e^{(t + \frac{1}{t})} \frac{d t}{t}$ , then