If f (x)= int(0)^(x) {f(t)}^(-1) dt and ...

If `f (x)= int_(0)^(x) {f(t)}^(-1) dt and int_(0)^(1) {f(t)}^(-1)= sqrt2`

`sqrt(2x)`

`sqrt(2 log_(e )x)`

`sqrt(3x-1)`

none of these

Text Solution

Verified by Experts

The correct Answer is:

We have,
f(f)`=overset(x)underset(0)int {f(t)}^(-1)dt`
`rArr f'(x)={f(t)}^(-1)`
`rArr f'(x)f(x)=1`
`rArr 2f(x)f'(x)=2 rArr{f(x)}^(2)=2x+C rArrf(x)=sqrt(2x+C)`b
Now,
`f(1)=sqrt(2)rArr sqrt(2)=sqrt(2+C) rArr C=0`
`:. F(x)=sqrt(x)`

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