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the range of thefunction y=[x 2 ] -[x] 2 , x belongs to [0,2] where [.] denotes the greatest integer function
When x lies in [0,1), x^2 lies in [0,1)So f(x)= 0-0^2=0When x lies in [1,√2), x^2 lies in [1,2)So f(x)= 1-1^2=0When x lies in [√2,√3), x^2 lies in [2,3)So f(x)= 2-1^2=1When x lies in [√3,2), x^2 lies in [3,4)So f(x)= 3-1^2=2When x=2, f(x)= 4-2^2=0Hence range of f(x) is {0,1,2}KINDLY APPROVE :))
Dear student Ans given by Aditya is not standard.Let x = t+1/2 Then [x] = t [x^2] = [t^2 + 1/4 +t] = t^2 + t[x2]−[x]2=tAs, t is an arbitrary integer, the range of the function is Z.
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