First slide

Functions (XII)

Question

The function $f (x) = x^{2} \log \frac{1 - x}{1 + x}$ is

Moderate

A

a periodic function
B

a bounded function
C

an odd function
D

an even function

Solution

$f (- x) = {(- x)}^{2} \log \frac{1 + x}{1 - x} = x^{2} \log {(\frac{1 - x}{1 + x})}^{- 1} = - x^{2} \log \frac{1 - x}{1 + x} = - f (x) .$

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