Question

Determine whether the following is even or odd

$f\left(x\right)=\log \left(\frac{1-x}{1+x}\right)$

• A. odd
• B. even
• C. neither even nor odd
• D. cannot be determined

Answer 1

The correct option is A odd

$f\left(x\right)=\log (1-x)-\log (1+x)$
$f(-x)=\log (1-(-x\left)\right)-\log (1-x)$
$=\log (1+x)-\log (1-x)$
$=-\left(\log \right(1-x)-\log (1+x\left)\right)$
$=-f\left(x\right)$
Hence, it is an odd function.