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

The function f(x) = (x + 1)/(x² − 9) is not continuous at which real values of x?

The function is discontinuous at x = 3 and x = −3. A rational function fails to be continuous where its denominator is zero, and x² − 9 equals zero at both these values. At x = −1 only the numerator vanishes, so continuity is unaffected.

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

Explanation

A rational function is continuous wherever its denominator is non-zero. Setting x² − 9 = 0 gives x = 3 or x = −3, where f is undefined. At x = −1 the numerator is zero, but the denominator is 1 − 9 = −8, so f(−1) = 0 and f is continuous there.

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