Question

Examine whether x((a^x+1)/(a^x-1) is an odd or even function

Answer 1

$f(x) = \frac{x( {a}^{x} + 1)}{( {a}^{x} - 1) }$
$f( - x) = \frac{ - x( {a}^{ - x} + 1)}{( {a}^{ - x} - 1) }$
on simplifying we get
$f( - x) = f(x)$
hence given function is even