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

The function f(x) = 1/(x² − 25) is discontinuous at which of the following sets of points?

The function is discontinuous at x = 5 and x = −5, because the denominator x² − 25 becomes zero at both points, so the function is undefined there. Everywhere else a rational function is continuous.

  1. Ax = 5 only
  2. Bx = −5 only
  3. Cx = 5 and x = −5Correct
  4. Dx = 0 only

Explanation

A rational function is discontinuous where its denominator is zero. x² − 25 = 0 gives x = 5 or x = −5. Choosing only one root misses the other point where the function is also undefined.

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