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f (x) is differentiable function satisfy...

f (x) is differentiable function satisfying the relationship `f ^(2) (x) + f ^(2) (y)+2 (xy-1) = f^(2) (x+y) AA x, y in R`
Also `f (x) gt 0 AA x in R and f (sqrt2)=2.` Then which of the following statement (s) is/are correct about `f (x)` ?

A

`[f (3)]=3([.]` denotes greatest integer function)

B

`f (sqrt7) =3`

C

` f (x)` is even

D

`f '(0)=0`

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The correct Answer is:
A, B, C, D
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