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Let f(x)=int(2)^(x)(dt)/(sqrt(1+t^(4))) ...

Let `f(x)=int_(2)^(x)(dt)/(sqrt(1+t^(4)))` and `g` be the inverse of `f` then the value of `g^(')(0)` is

A

`1`

B

`17`

C

`sqrt(17)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=int_(2)^(x)(dt)/(sqrt(1+t^(4)))`
`implies f'(x)=1/(sqrt(1+x^(4)))=(dy)/(dx)`
Now `g'(x)=(dx)/(dy)=sqrt(1+x^(4))`
when `y=0`, ie. `int_(2)^(x)(dt)/(sqrt(1+t^(4)))=0` then `x=2`
`:. g'(0)=sqrt(1+16)=sqrt(17)`
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