Given the function f (x) = x (1 / (2 ^ x-1) + 1 / 2), ask: prove that it is even function

Given the function f (x) = x (1 / (2 ^ x-1) + 1 / 2), ask: prove that it is even function

The standard of even function is f (x) = f (- x) f (- x) = (- x) {1 / [2 ^ (- x) - 1] + 1 / 2} = (- x) {1 / [(1 / 2) ^ X-1] + 1 / 2} = (- x) {1 / [(1-2 ^ x) / 2 ^ x + 1 / 2} = (- x) [2 ^ X / (1-2 ^ x) + 1 / 2] = (- x) (2 * 2 ^ x + 1-2 ^ x) / 2 (2 ^ x-1)] (1) f (x) = x (1 / (2 ^ x-1) + 1 / 2) = x [