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})

f (x) = 3 (x - 1)^{2} - 5

f (x) = x^{2} - 4 x + 17

f (x) = 0.25 x

f (x) = \frac{2 x - 3}{x + 3}

9 y - 8

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))