Let $f:[-1,2] \to \mathbb{R}$ be defined by $f(x) = [x^2-3]$ where $[.]$ denotes greatest integer function, then the number of points of discontinuity for the function $f$ in $(-1,2)$ is
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The greatest integer function $[f(x)]$ is discontinuous whenever $f(x)$ is an integer, with a key exception: if $f(x)$ merely touches an integer value at a local minimum or maximum without crossing it, the function may be continuous at that point.