Question

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

• A. even
• B. periodic
• C. odd
• D. neither even nor odd

Answer 1

Answer: (A)

$f(-x)=\frac{-x}{e^x-1}-\frac{x}{2}+1$
$=\frac{-x{e}^x}{1-e^x}-\frac{x}{2}+1$
$=\frac{x\left(e^x-1+1\right)}{e^x-1}-\frac{x}{2}+1$
$=\frac{x}{e^x-1}+\frac{x}{2}+1=f(x)$