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If $f(x)=[x]^2-[x^2]$, (where [.] denotes the greatest integer function), and x ∈ [0, 2] then the range of f(x) is |
{−1, 0, 2} {0, 1, 2} {−2, −1, 0} [−2, 0, 1} |
{−2, −1, 0} |
$f(x)=[x]^2-[x^2]=\left\{\begin{matrix}0,&0≤x<\sqrt{2}\\-1,&\sqrt{2}≤x<\sqrt{3}\\-2,&\sqrt{3}≤x<2\\0,&x=2\end{matrix}\right.$ ∴ Range of f(x) is {−2, −1, 0}. |
