Description for Correct answer:
We have \( \Large f \left(x\right)=log \left(x+\sqrt{x^{2}+1}\right) \)

=> \( \Large f \left(-x\right)=log \left(-x+\sqrt{x^{2}+1}\right) \)

\( \Large \therefore f \left(x\right)+f \left(x\right)=log \left(x+\sqrt{x^{2}+1}\right)+log \left(-x+\sqrt{x^{2}+1}\right) \)

= \( \Large log \left(1\right) = 0 \)

Hence, \( \Large f \left(x\right) \) is an odd function.