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Let f:R to R and g:R to R be functions d...

Let `f:R to R` and `g:R to R` be functions defined by `f(x)=sgn (sin x),g(x)=sin(sgn x)` where
`sgn alpha={{:(1,,"if "alpha gt 0),(-1,,"if "alpha gt 0),(0,,"if "alpha=0):}`
If `A=f'(pi)` and `B=g'(pi)`, then

A

A does not exist and B = 0

B

A = 0 and B = 0

C

both A and B do not exist

D

A = 0 and B does not exist

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The correct Answer is:
A
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