AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper

The function is given as.
f(x)=[2x]−2[x] for x∈R
The x is comes out as.
x=[x]+{x}
2x=2[x]+2{x}
[2x]=2[x]+(2[x])
The range for function 2x is,
[2x]={

2[x]+0,0<{x}< 1 2

2[x]+1, 1 2 ≤{x}<1

Putting the values in given function.
[2x]−2[x]={

0,	0≤{x}< 1 2
1,	1 2 ≤{x}<1

Thus, the range of the function is {0,1}.