Q82 / 120 · NDA 2024 (Phase 2) · Mathematics

Paragraph: Let $f \circ g(x)=\cos ^2 \sqrt{x}$ and $g \circ f(x)=|\cos x|$.
Question: Which one of the following is $g(x)$ ?

  • Correct answer
    A
    $\sqrt{x}$
  • B
    $|x|$
  • C
    $x^2$
  • D
    $x|x|$

Solution

If $\mathrm{f}(\mathrm{x})=\cos ^2 \mathrm{x}$ then $\mathrm{g}(\mathrm{x})=\sqrt{\mathrm{x}}$, so that fog $(x)=\cos ^2 \sqrt{x}$

Hence, the correct answer is option: 'A'.

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