Q. The function $f(x) = \log{(x + \sqrt{x^{2} + 1})}$ is
A) An even function
B) An odd function
C) A periodic function
D) Neither an even nor an odd function
Explanation
(b)
Given, $f(x) = \log\left( x + \sqrt{x^{2} + 1} \right)$
$\therefore\ \ f(x) + f( - x) = \log{(x + \sqrt{x^{2} + 1} + \log{( - x + \sqrt{x^{2} + 1}})}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \log{(1) = 0}$
Hence, $f(x)$ is an odd function.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.