A) neither an even nor an odd function
B) an even function
C) an odd function
D) a periodic function
Correct Answer: C
Solution :
[c] \[f(x)=log(x+\sqrt{{{x}^{2}}+1})\] \[f(-x)=log\left\{ -x+\sqrt{{{x}^{2}}+1} \right\}=\log \left\{ \frac{-{{x}^{2}}+{{x}^{2}}+1}{x+\sqrt{{{x}^{2}}+1}} \right\}\] \[=-\log (x+\sqrt{{{x}^{2}}+1})=-f(x)\Rightarrow f(x)\] is an odd function.
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