How do you find the inverse of $y=e^x/(1+6e^x)$ ?

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Answer 1 · 2015-12-06T04:45:33

$y=ln(x/(1-6x))$

Switch $x$ and $y$ then solve for $y$ .

$x=e^y/(1+6e^y)$

$x(1+6e^y)=e^y$

$x+6xe^y=e^y$

$6xe^y-e^y=-x$

$e^y(6x-1)=-x$

$e^y=-x/(6x-1)$

$e^y=x/(1-6x)$

$ln(e^y)=ln(x/(1-6x))$

$yln(e)=ln(x/(1-6x))$

$y=ln(x/(1-6x))$

How do you find the inverse of y=e^x/(1+6e^x)y=e^x/(1+6e^x)?