Question

Dê a função inversa:

y = (e^x)/(1 + 2e^x)

Answer 1

$y=\dfrac{e^{x}}{1+2e^{x}}$

$x=\dfrac{e^{y}}{1+2e^{y}}$

$x+x\cdot2e^{y}=e^{y}$

$e^{y}-x\cdot2e^{y}=x$

$e^{y}\cdot(1-2x)=x$

$e^{y}=\dfrac{x}{1-2x}$

$y\cdot\log e=\log\left(\dfrac{x}{1-2x}\right)$

$y=\dfrac{\log\left(\dfrac{x}{1-2x}\right)}{\log e}$