f(x)=[x-1/2]+[x+1/2]+2[-x]range of the function?

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.
 
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Askiitians Experts
Badiuddin