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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

How many points of discontinuity does the function f(x) = (x − 2)/(x² − 3x + 2) have on the real line?

There are 2 points of discontinuity, x = 1 and x = 2. The denominator (x − 1)(x − 2) is zero at both, so f is undefined there. The cancellation at x = 2 only makes that discontinuity removable; it does not make f continuous at that point.

  1. A0
  2. B1
  3. C2Correct
  4. D3

Explanation

Factorising, x² − 3x + 2 = (x − 1)(x − 2). The function is undefined at x = 1 and at x = 2. Although the factor (x − 2) cancels at x = 2, f is still not defined there, so it is discontinuous (removable) at x = 2, as well as at x = 1. Hence there are 2 points.

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