The range of the function `y=[x^2]-[x]^2` `x in [0,2]` (where [] denot – InterviewSolution

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1.	The range of the function `y=[x^2]-[x]^2` `x in [0,2]` (where [] denotes the greatest integer function), isA. [0]B. [0,1]C. [1,2]D. [0,1,2]
Answer» Correct Answer - D We have, `{:(,y=[x^(2)]-[x]^(2)",",x in[0,2]),("i.e.,",y=[x^(2)]",",0lexlt1),(,y=[x^(2)]-1",",1lexlt2),(,y=0,x=2),("i.e.,",y=0",",0lexlt1),(,=1-1=0",",1lexltsqrt2),(,=2-1=1",",sqrt2lexltsqrt3),(,=3-1=2",",sqrt2lexltsqrt3),(,=3-1=2",",sqrt3lexlt2),(,=0,x=2):}` Hence, the range is `{0,1,2}.`

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