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NDA 1 2025 Maths, question 85

Topic: Differential calculus

Passage · Q85 to Q86

Let the curve f(x)=∣x−3∣f(x) = |x - 3|.

Q85

What is the domain of the function f(x)f(x)?

  1. (a) (0,∞)(0,\infty)
  2. (b) (3,∞)(3,\infty)
  3. (c) (−∞,∞)( - \infty,\infty)Correct answer
  4. (d) (−∞,∞)∖{3}( - \infty,\infty) \smallsetminus \{ 3\}

Solution.

Answer: (c) (−∞,∞)( - \infty,\infty)

  1. The expression x−3x - 3 is defined for every real xx, and taking an absolute value creates no restriction.
  2. In particular, f(3)=0f(3) = 0 is valid.