Question:medium

Let the function $f(x)$ be defined as \[ f(x)=\frac{x-|x|}{x} \] then:

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Whenever modulus functions appear, always split the problem into two cases: \[ x>0 \quad \text{and} \quad x<0. \] This immediately reveals continuity and differentiability behavior.
Updated On: May 16, 2026
  • the function is continuous everywhere
  • the function is not continuous
  • the function is continuous when $x<0$
  • the function is continuous for all $x$ except zero
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The Correct Option is D

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