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Grade: 12

                        

the range of thefunction y=[x 2 ] -[x] 2 , x belongs to [0,2] where [.] denotes the greatest integer function

6 months ago

Answers : (2)

Aditya Gupta
2065 Points
							
When x lies in [0,1), x^2 lies in [0,1)
So f(x)= 0-0^2=0
When x lies in [1,√2), x^2 lies in [1,2)
So f(x)= 1-1^2=0
When x lies in [√2,√3), x^2 lies in [2,3)
So f(x)= 2-1^2=1
When x lies in [√3,2), x^2 lies in [3,4)
So f(x)= 3-1^2=2
When x=2, f(x)= 4-2^2=0
Hence range of f(x) is {0,1,2}
KINDLY APPROVE :))
6 months ago
Vikas TU
12278 Points
							
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=t
As, t is an arbitrary integer, the range of the function is Z.
6 months ago
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