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})

\frac{2 x - 1}{x - 1}

lo g_{10} (4.8)

f (x) = \frac{4 x + 2}{5 x - 5}

3 - s - 2 + s

y = (x + 4)^{4} + 3, x \geq - 4

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))