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Limits Continuity and Differentiability question

2023 · 11 Apr · Shift 1 · Q34

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JEE Main
Mathematics
Limits Continuity and Differentiability
2023 · 11 Apr · Shift 1 · Q34

Limits Continuity and Differentiability question

2023 · 11 Apr · Shift 1 · Q34

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f(x)=\left[x^{2}-x\right]+|-x+[x]|

, where

x \in \mathbb{R}

and

[t]

denotes the greatest integer less than or equal to

t

. Then,

f

is :

A
continuous at $x=0$ , but not continuous at $x=1$
B
continuous at $x=0$ and $x=1$
C
continuous at $x=1$ , but not continuous at $x=0$
D
not continuous at $x=0$ and $x=1$

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