Let f(x)=|x|+[x−1], where [.] is greatest integerfunction, then f(x) is

Let $f (x) = | x | + [x - 1]$ , where $[.]$ is greatest integer
function, then $f (x)$ is

A
continuous at $x = 0$ as well as at $x = 1$
B
continuous at $x = 0$ but not at $x = 1$
C
continuous at $x = 1$ but not at $x = 0$
D
neither continuous at $x = 0$ or nor at $x = 1$

Solution:

$[x]$ is not continuous at $x \in I and | x |$ is a continuous
function so $| x | + [x - 1] ∣$ is neither continuous at $x = 0$

nor at $x = 1 .$

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