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GATE 2016 ME (ME2) – Question 12

Engineering Mathematics · Calculus: Limit, continuity, differentiability, mean value theorems and indeterminate forms · 1 mark · Multiple choice

$f(x)=(x^2-3x-4)/(x^2+3x-4)$ is not continuous at ______.

  1. 4 and −1
  2. 4 and 1
  3. −4 and 1
  4. −4 and −1

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Correct answer: (C) −4 and 1

Explanation

The denominator factors as x²+3x−4=(x+4)(x−1), so the expression is undefined at−4 and1. The numerator(x−4)(x+1) cancels neither denominator factor. These are the discontinuities, **C**. Roots of the numerator alone do not cause discontinuity.