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

The domain of the real function f(x) = (2x − 3)/(x² − 5x + 6) is:

The denominator x² − 5x + 6 factors as (x − 2)(x − 3), so it is zero at x = 2 and x = 3. The function is undefined at only these points, so the domain is all real numbers except 2 and 3.

  1. AR − {2, 3}Correct
  2. BR − {−2, −3}
  3. CR − {3/2}
  4. DR − {2, 3, 3/2}

Explanation

The function is undefined where the denominator is zero. Since x² − 5x + 6 = (x − 2)(x − 3), it vanishes at x = 2 and x = 3. The numerator being zero at x = 3/2 only makes f(x) zero there, so 3/2 stays in the domain.

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