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
Correct Answer: D
Solution :
Here, \[f(x)=\log \left( \frac{1+x}{1-x} \right)\] and \[f(-x)=\log \left( \frac{1-x}{1+x} \right)=\log {{\left( \frac{1+x}{1-x} \right)}^{-1}}\] \[=-\log \left( \frac{1+x}{1-x} \right)=-f(x)\] Þ \[f(x)\] is an odd function.
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