Skip to content

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

The function f(x) = (x² − 25)/(x − 5) for x ≠ 5, and f(5) = 8. Which statement about f at x = 5 is correct?

The function is discontinuous at x = 5. For x not equal to 5 it simplifies to x + 5, so the limit at 5 is 10, but the defined value f(5) is 8. Continuity requires the limit to equal the function value, which fails here.

  1. Af is continuous at x = 5 because f(5) is defined
  2. Bf is discontinuous at x = 5 because the limit is 10 but f(5) = 8Correct
  3. Cf is discontinuous at x = 5 because the limit does not exist
  4. Df is continuous at x = 5 because the limit is 8

Explanation

For x ≠ 5, f(x) = x + 5, so the limit as x → 5 is 10. But f(5) = 8, which differs from the limit. Continuity needs limit = function value, so f is discontinuous. Option 1 is wrong because merely being defined at the point is not enough.

Did you get it right without looking?

One question tells you little. A timed set on Sets, Relations and Functions, Limits and Continuity shows your real accuracy, how long you take and where you lose marks.

Practise Sets, Relations and Functions, Limits and ContinuityFree diagnostic mock

More Sets, Relations and Functions, Limits and Continuity questions