Inverse function (1 Viewer)

Kipling · May 8, 2013

Don't know why but I can't seem to find the inverse function of: f(x) = (e^x) / 3+(e^x)

Sy123 · May 8, 2013

$y = \frac{e^x}{3+e^x}$

$3y + y \cdot e^x = e^x$

$3y = e^x(1-y)$

$e^x = \frac{1-y}{3y}$

$\therefore \ f^{-1}(x) = \ln \left |\frac{1-x}{3x} \right |$

HeroicPandas · May 8, 2013

sorry u have made a little mistake!

$3y = e^x (1-y)$

$e^x = \frac{3y}{1-y}$

Carrotsticks · May 8, 2013

Sy123 said:
$y = \frac{e^x}{3+e^x}$

$3y + y \cdot e^x = e^x$

$3y = e^x(1-y)$

$e^x = \frac{1-y}{3y}$

$\therefore \ f^{-1}(x) = \ln \left |\frac{1-x}{3x} \right |$

Adding the absolute value sign made your solution incorrect. You in a sense 'extended the domain', which in a sense 'ruined' its monotonicity.

Without absolute values:

With absolute values:

Sy123 · May 8, 2013

HeroicPandas said:
sorry u have made a little mistake!

$3y = e^x (1-y)$

$e^x = \frac{3y}{1-y}$

Carrotsticks said:
Adding the absolute value sign made your solution incorrect. You in a sense 'extended the domain', which in a sense 'ruined' its monotonicity.

Without absolute values:

With absolute values:

Yes silly me, thanks.

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Inverse function (1 Viewer)

Kipling

New Member

Sy123

This too shall pass

HeroicPandas

Heroic!

Carrotsticks

Retired

Sy123

This too shall pass

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