Question

Inverse function of y = e^x/(1+e^x)

Answer 1

\[y = e^x/(1+e^x)\]

Answer 2

How do I solve for x?

Answer 3

Order all by normalizing in compared to e^x and you get\[e ^{x} (1-y) = y \] Than just devide by (1-y) take a logirthm and solve for x.

Answer 4

@Botev what do you mean by normalizing?

Answer 5

\(\large y = \frac{e^x}{1+e^x} \rightarrow \frac{1}{y}=\frac{1+e^x}{e^x} \)
\(\large \frac{1}{y}=\frac{1+e^x}{e^x} = \frac{1}{e^x}+\frac{e^x}{e^x}=e^{-x}+1 \)
\(\large \frac{1}{y}-1=e^{-x} \rightarrow \frac{1-y}{y}=e^{-x} \)
can you take it from here to solve for x?

Answer 6

yes, thank you dpalnc!