Question

Find whether $f\left(x\right)=\frac{a^x+1}{a^x-1}$ is even, odd or neither odd nor even.

Answer 1

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

$f(-x)=\frac{a^{-x}+1}{a^{-x}-1}$

$f(-x)=\frac{\frac{1}{a^x}+1}{\frac{1}{a^x}-1}$

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

Thus $f\left(x\right)$ is an odd function