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f(x)=[x-1/2]+[x+1/2]+2[-x]
let x=I +f
where I is integer part of x and 0<= f<1
f(x) =[I+f-1/2]+[I+f+1/2]+2[-I-f]
=I +[f-1/2] + I +[f+1/2] -2I +2[-f]
f(x)=[f-1/2]+[f+1/2]+2[-f]
case 1 0=< I <1/2
f(x)= -1 +0 -2 =-3
case 2 1/2=< I <1
f(x) = 0 +1 -2 =-1
so range is -1 and -3
All the best. Regards,Askiitians ExpertsBadiuddin
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