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NDA 2 2024 Maths, question 81

Topic: Algebra

Passage · Q81 to Q82

Let f∘g(x)=cos⁡2xf\circ g(x)=\cos ^{2}\sqrt{x} and g∘f(x)=∣cos⁡x∣g\circ f(x)=|\cos x|.

Q81

Which one of the following is f(x)f(x)?

  1. (a) cos⁡x\cos x
  2. (b) cos⁡x2\cos x^{2}
  3. (c) cos⁡2x\cos ^{2}xCorrect answer
  4. (d) cos⁡∣x∣\cos |x|

Solution.

Answer: (c) cos⁡2x\cos ^{2}x

  1. The supplied choices fit f(x)=cos²x and g(x)=√x.
  2. Substitution gives f(g(x))=cos²√x for x≥0 and g(f(x))=√(cos²x)=|cos x|.
  3. Thus (c) is the matching f; the absolute value is essential.