Question

If $f\left(x\right)=\log (x+\sqrt{1+x^2})$ then $f\left(x\right)$ is

• A. Periodic
• B. Even function
• C. Odd function
• D. None o fthese

Answer 1

Answer: (C)

Odd function

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