Question

Is the function $f\left(x\right)=\frac{x(a^x+1)}{a^x-1}$ odd or even

• A. even
• B. odd
• C. neither even nor odd
• D. even for only some values of $x$ is domain

Answer 1

Answer: (A)

even

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