Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be an odd function and suppose $f\left(e^x\right)=e^{f(x)}$ for all $x \in \mathbb{R}$. Then

• Correct answer
  A

  $f(1 / e) \lt f(1) \lt f(e)$
• B

  $f(1 / e) \gt f(1) \gt f(e)$
• C

  $f(1) \lt f(1 / e) \lt f(e)$
• D

  $f(1) \gt f(1 / e) \gt f(e)$

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