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NDA 2018 Maths · Mathematics · Sets, Relations and Functions · easy

What is the domain of the real function f(x)=(√(x-2))/(x-5)?

Single correct option

What is the domain of the real function f(x)=x−2x−5f(x)=\dfrac{\sqrt{x-2}}{x-5}?
  1. A. (2,∞)∖{5}(2,\infty)\setminus\{5\}
  2. B. [2,∞)∖{5}[2,\infty)\setminus\{5\}
  3. C. [2,∞)[2,\infty)
  4. D. R∖{5}\mathbb{R}\setminus\{5\}
Show answer and solution

Answer: (B) [2,∞)∖{5}[2,\infty)\setminus\{5\}

The square root needs x−2≥0x-2\ge 0, so x≥2x\ge 2 (and x=2x=2 is allowed because the root of 0 is defined). The denominator vanishes at x=5x=5, which must be removed. Domain =[2,∞)∖{5}=[2,\infty)\setminus\{5\}. Option with the open interval wrongly drops x=2x=2.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake