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