Question

若f(x)=lg[2x/(1+x)+a]是奇函数,求a的值

Answer 1

f(-x)+f(x)=0 ,lg [(a+2)x+a] / (1+x) + lg [(a+2)(-x)+a] / (1-x) = 0

=> [(a+2)x+a] / (1+x) * [(a+2)(-x)+a] / (1-x) = 1

=> a^2 - (a+2)^2 x^2 = 1 - x^2

=> a = -1