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Let f:(0,oo)rarrRR be given by f(x)=ov...

Let `f:(0,oo)rarrRR` be given by
`f(x)=oversetxunderset(1/x)inte^((t+1/t))dt/t`
Then

A

f(x) is monotonically increasing on `[1,oo)`

B

f(x) is monotonically decreasing on (0,1]

C

`f(x)+f(1/x)=0`, for all `x in(0,oo)`

D

`f(2^x)` is ann odd function of x on `RR`

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The correct Answer is:
A, C, D
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