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Iff(x)=1+1/xint1^xf(t)dt ,t h e nt h ev ...

`Iff(x)=1+1/xint_1^xf(t)dt ,t h e nt h ev a l u eof(e^(-1))i s` 1 (b) 0 (c) `-1` (d) none of these

A

`1`

B

`0`

C

`-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given `xf(x)=x+int_(1)^(x)f(t)dt`…………….1
`f(x)+xf'(x)=1+f(x)`
`=f'(x)=1/x`
or `f(x)=log|x|+c`
`f(1)=1`
or `f(x)=log|x|+1`
or `f(e^(-1))=0`
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