Question

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

• A. An even function
• B. An odd function
• C. A periodic function
• D. neither an even nor odd function

Answer 1

The correct option is A An even function

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