Functions Question 223
Question: If $ f(x)=\log \frac{1+x}{1-x} $ , then $ f(x) $ is
[Kerala (Engg.) 2002]
Options:
A) Even function
B) $ f(x_1)f(x_2)=f(x_1+x_2) $
C) $ \frac{f(x_1)}{f(x_2)}=f(x_1-x_2) $
D) Odd function
Show Answer
Answer:
Correct Answer: D
Solution:
Here, $ f(x)=\log ( \frac{1+x}{1-x} ) $ and $ f(-x)=\log ( \frac{1-x}{1+x} )=\log {{( \frac{1+x}{1-x} )}^{-1}} $ $ =-\log ( \frac{1+x}{1-x} )=-f(x) $
Þ $ f(x) $ is an odd function.
BETA
