If f(x) = sqrt((sqrt(x-1)-2)^2)+sqrt((sq...

If f(x) = `sqrt((sqrt(x-1)-2)^2)+sqrt((sqrt(x-1)-3)^2)` , then f '(2) is equal to :

A

2

B

`-2`

C

1

D

`-1`

Verified by Experts

The correct Answer is:

D

`f(x)=sqrt(((sqrt(x-1))-2)^(2))+sqrt(((sqrt(x-1))-3)^(2))`
`= |sqrt(x-1)-2|+|sqrt(x-1)-3|`
`therefore f'(2)=-(1)/(sqrt(x-1))` & put x = 2

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