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Question: Answered & Verified by Expert
The function $f(x)=\log \left(x+\sqrt{x^2+1}\right)$, is
MathematicsFunctionsJEE MainJEE Main 2003
Options:
  • A
    neither an even nor an odd function
  • B
    an even function
  • C
    an odd function
  • D
    a periodic function
Solution:
2763 Upvotes Verified Answer
The correct answer is:
an odd function
$f(x)=\log \left(x+\sqrt{x^2+1}\right)$
$f(-x)=-\log \left(x+\sqrt{x^2+1}\right)$
$f(-x)=-f(x)$, i.e., $f(x)$ is an odd function.

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