Q113 / 180 · COMEDK 2014 · Mathematics

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

  • A
    an even function.
  • Correct answer
    B
    an odd function.
  • C
    a periodic function.
  • D
    neither an even nor an odd function.

Solution

Given, $f(x)=\log \left(x+\sqrt{x^{2}+1}\right)$ $\therefore \quad f(x)+f(-x)=\log \left(x+\sqrt{x^{2}+1}\right)$ $\quad+\log \left(-x+\sqrt{x^{2}+1}\right)=\log (1)=0$ $\Rightarrow \quad f(-x)=-f(x)$ Hence, $f(x)$ is an odd function.

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

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