If f(x) = e^x – 1/ e^x +1 for all real values of x, prove that f(-x) = -f(x).

Answer 1

f(-x) = (e^-x - 1)/(e^-x+1)
= (1/e^x - 1)/(1/e^x + 1)
= (1-e^x)/(1+e^x)
= -f(x)