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NDA 2 2025 Maths, question 81

Topic: Differential calculus

Passage · Q81 to Q82

Consider the function f(x)=1−(x−1)23f(x)=1-\sqrt[3]{(x-1)^{2}}.

Q81

What is the domain of the function?

  1. (a) (1,∞)(1,\infty )
  2. (b) (−∞,∞)(-\infty ,\infty )Correct answer
  3. (c) (0,∞)(0,\infty )
  4. (d) (−∞,∞)∖(-\infty ,\infty )∖ {11}

Solution.

Answer: (b) (−∞,∞)(-\infty ,\infty )

  1. The cube root of (x−1)² is defined for every real x.
  2. No denominator or even-root restriction appears, so the domain is all real numbers.