Consider the function f(x)=[x]+|1-x|, -1 x3, where [x] is the greatest integer function.

Question

Consider the function $f(x)=[x]+|1-x|$, $-1\le x\le3$, where $[x]$ is the greatest integer function.

Statement 1: $f$ is not continuous at $x=0,1,2$ and $3$.

Statement 2: $f(x)=\begin{cases}-x, & -1\le x<0\1-x, & 0\le x<1\1+x, & 1\le x<2\2+x, & 2\le x\le3\end{cases}$

Accepted Answer

$f$ is actually not continuous at $x=0,1,2$, but is continuous at $x=3$ (endpoint, no jump beyond domain). So Statement 1 (claiming discontinuity at $x=3$ too) is false, while Statement 2's piecewise formula is correct.

Solutions · 1