Find the inverse of a function

Question

f (x) = (2^x)/(1+2^x)

Answer 1

Let y=f(x)=2ˣ/(1+2ˣ)=1/(2⁻ˣ+1).

So 2⁻ˣ+1=1/y, 2⁻ˣ=1/y-1=(1-y)/y, 2ˣ=y/(1-y).

Taking logs to base 2:

x=log₂(y/(1-y)) or log₂(y)-log₂(1-y).

So the inverse f⁻¹(x)=log₂(x/(1-x)).