At how many points in $[0, 3]$ is $f(x) = x - [x]$ not continuous?

0

Correct answerYour answer

2

Correct answerYour answer

3

Correct answerYour answer

4

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$x - [x]$ drops from almost 1 to 0 at each integer, from the right side.
On $[0, 3]$ the break is at 1, 2 and 3; at 0 only the right side counts, and there it is continuous.

Worth noting

4 also counts 0, where the interval begins and only the right-hand limit matters.

Ten questions from Continuity & Differentiability, at your own pace.

Ten questions from Continuity & Differentiability, at your own pace.

At how many points in [0,3][0, 3][0,3] is f(x)=x−[x]f(x) = x - [x]f(x)=x−[x] not continuous?