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Let f: R->R be the signum function defin...

Let `f: R->R` be the signum function defined as `f(x)={1,\ x >0,\ \ \ \ 0,\ x=0,\ \ \ \ \-1,\ x<0` and `g: R->R` be the greatest integer function given by `g(x)=[x]` . Then, prove that `fog` and `gof` coincide in `[-1,\ 0)` .

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