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Let f : R to R be the Signum Function de...

Let `f : R to R` be the Signum Function defined as
` f (x) = {{:(1",", x gt 0), ( 0"," , x =0), ( -1 "," , x lt 0):}`
and `g : R to R` be the Greatest Integer Function given by `g (x) = [x],` where `[x]` is greatest integer less than or equal to x. Then does fog and gof coincide in `(0,1]`?

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The correct Answer is:
NO
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