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If f (x) be a differentiable function sa...

If `f (x)` be a differentiable function satisfying `f (y) f ((x)/(y))=f (x) AA, x y in R, y ne 0 and f (1) ne 0,f (1) =3,` then

A

sgn `(f(x))` is non-differentiable at exactly one point

B

`lim _(xto0)(x ^(2) (cos x-1))/(f (x))=0`

C

`f (x) =x` has 3 solutions

D

`f (f(x))-f ^(3) (x)=0` has infinitely many solutions

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A, B, C, D
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