What is the inverse of f(x)=(e^x)/(1+6e^x) ?

The inverse of f(x)=(e^x)/(1+6e^x) is ln(-x/(6x-1))

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inverse of f(x)=(e^x)/(1+6e^x)

inverse

f (x) = \frac{e ^{x}}{1 + 6 e ^{x}}

ln (- \frac{x}{6 x - 1})

Solution steps

y = \frac{e ^{x}}{1 + 6 e ^{x}}

Replace

x

with

y

x = \frac{e ^{y}}{1 + 6 e ^{y}}

Solve for

y, x = \frac{e ^{y}}{1 + 6 e ^{y}}

ln (- \frac{x}{6 x - 1})

2 x + 3 + 1

(1, 0), (1, - 3)

f (x) = 4 (x + 1)

\frac{x ^{2} - x - 3}{x + 1}

\frac{5 x}{x + 3}

What is the inverse of f(x)=(e^x)/(1+6e^x) ?
The inverse of f(x)=(e^x)/(1+6e^x) is ln(-x/(6x-1))