jee-main 2019 Q80

jee-main · India · session2_08apr_shift2 Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions
Let $f : [ - 1,3 ] \rightarrow \mathrm { R }$ be defined as $$f ( x ) = \begin{cases} |x| + [x], & -1 \leq x < 1 \\ x + |x|, & 1 \leq x < 2 \\ x + [x], & 2 \leq x \leq 3 \end{cases}$$ where $[t]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is discontinuous at:
(1) Only one point
(2) Only two points
(3) Four or more points
(4) Only three points
Let $f : [ - 1,3 ] \rightarrow \mathrm { R }$ be defined as
$$f ( x ) = \begin{cases} |x| + [x], & -1 \leq x < 1 \\ x + |x|, & 1 \leq x < 2 \\ x + [x], & 2 \leq x \leq 3 \end{cases}$$
where $[t]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is discontinuous at:\\
(1) Only one point\\
(2) Only two points\\
(3) Four or more points\\
(4) Only three points