Q222 / 270 · NDA 2017 (Phase 2) · Mathematics

The function $f(x)=|x|-x^3$ is

  • A
    odd
  • B
    even
  • C
    both even and odd
  • Correct answer
    D
    neither even nor odd

Solution

$\begin{aligned} & f(x)=|x|-x^3 \\ & f(x)=\left\{\begin{array}{l}x-x^3, x \geq 0 \\ -x-x^3, x \lt 0\end{array} \quad f(-x)=\left\{\begin{array}{l}x+x^3, x \geq 0 \\ x+x^3, x \lt 0\end{array}\right.\right.\end{aligned}$ Neither even nor odd.

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

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