iran-konkur 2013 Q115

iran-konkur · Other · konkur-riazi_1392 Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions
115- If $f(x) = [x] + [-x]$ and $g(x) = \begin{cases} f(x) & ; \ x \notin \mathbb{Z} \\ f(x) - 1 & ; \ x \in \mathbb{Z} \end{cases}$, then the number of points of discontinuity of $g$ on the interval $[4, -4]$ is which of the following?
(1) $1$ (2) $2$ (3) $3$ (4) zero
115- If $f(x) = [x] + [-x]$ and $g(x) = \begin{cases} f(x) & ; \ x \notin \mathbb{Z} \\ f(x) - 1 & ; \ x \in \mathbb{Z} \end{cases}$, then the number of points of discontinuity of $g$ on the interval $[4, -4]$ is which of the following?

(1) $1$ \hfill (2) $2$ \hfill (3) $3$ \hfill (4) zero