Functions Question 435
Question: The function $ f(x)=log( x+\sqrt{x^{2}+1} ) $ , is
Options:
A) neither an even nor an odd function
B) an even function
C) an odd function
D) a periodic function
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ f(x)=log(x+\sqrt{x^{2}+1}) $ $ f(-x)=log{ -x+\sqrt{x^{2}+1} }=\log { \frac{-x^{2}+x^{2}+1}{x+\sqrt{x^{2}+1}} } $ $ =-\log (x+\sqrt{x^{2}+1})=-f(x)\Rightarrow f(x) $ is an odd function.
BETA
