The function $f(x)=|x-1|, x \in R$ is :

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The function $f(x)=|x-1|, x \in R$ is :

Options:

Continuous at x=1, but not differentiable at x=1

Discontinuous at x=1, but differentiable at x=1

Continuous and differentiable at x=1

Neither continuous nor differentiable at x=1

Correct Answer:

Continuous at x=1, but not differentiable at x=1

Explanation:

graph of $|x-1|$

from graph it is continuous at $x=1$

while not differentiable due to sharp point