Question

The inverse of function $y=\frac{2^x}{1+2^x}$ is :

• A. $x={\log }_2\frac{y}{1-y}$
• B. $x={\log }_2\frac{1}{1-2^y}$
• C. $x={\log }_2(1-\frac{1}{y})$
• D. $x={\log }_2\left(\frac{1}{1-y}\right)$

Answer 1

The correct option is A $x={\log }_2\frac{y}{1-y}$

$y=\frac{2^x}{1+2^x}\Rightarrow y=1-\frac{1}{1+2^x}\Rightarrow \frac{1}{1-y}-1=2^x\Rightarrow \frac{y}{1-y}=2^x\Rightarrow x={\log }_2\frac{y}{1-y}$