If the function $f:R\to A$ defined as $f\left(x\right)={\tan }^{-1}\left(\frac{2x^3}{1+x^6}\right)$ is a surjective function, then the set $A$ is equal to

• A

  $\left[–\frac{\pi }{2},\frac{\pi }{2}\right]$
• Correct answer
  B

  $\left[–\frac{\pi }{4},\frac{\pi }{4}\right]$
• C

  $\left(–\frac{\pi }{2},\frac{\pi }{2}\right)$
• D

  $\left[0,\frac{\pi }{4}\right]$

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