What is the inverse of f(x)=(e^x)/((1+7e^x)) ?

The inverse of f(x)=(e^x)/((1+7e^x)) is ln(-x/(7x-1))

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inverse of f(x)=(e^x)/((1+7e^x))

inverse

f (x) = \frac{e ^{x}}{( 1 + 7 e ^{x} )}

ln (- \frac{x}{7 x - 1})

Solution steps

y = \frac{e ^{x}}{1 + 7 e ^{x}}

Replace

x

with

y

x = \frac{e ^{y}}{1 + 7 e ^{y}}

Solve for

y, x = \frac{e ^{y}}{1 + 7 e ^{y}}

ln (- \frac{x}{7 x - 1})

y = 2 x + 3

y = \frac{x + 3}{x ^{4} - 81}

h (x) = \frac{x ^{2} + 7}{x ^{2} + 2 x - 48}

\frac{2 x ^{2} - 5 x + 5}{x - 2}

cos (x) - 1

What is the inverse of f(x)=(e^x)/((1+7e^x)) ?
The inverse of f(x)=(e^x)/((1+7e^x)) is ln(-x/(7x-1))