Question

Choose the correct option: $x\frac{a^x+1}{a^x-1}$ is

• A. odd function
• B. even function
• C. both odd and even
• D. neither odd nor even

Answer 1

The correct option is B even function

$f(-x)=(-x)\frac{a^{-x}+1}{a^{-x}-1}=-x\frac{1+a^x}{1-a^x}$ $=x\frac{a^x+1}{a^x-1}=f\left(x\right)$
Hence $f\left(x\right)$ is an even function