What is the inverse of f(x)=(e^x)/(1+4e^x) ?

The inverse of f(x)=(e^x)/(1+4e^x) is ln(-x/(4x-1))

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inverse of f(x)=(e^x)/(1+4e^x)

inverse

f (x) = \frac{e ^{x}}{1 + 4 e ^{x}}

ln (- \frac{x}{4 x - 1})

Solution steps

y = \frac{e ^{x}}{1 + 4 e ^{x}}

Replace

x

with

y

x = \frac{e ^{y}}{1 + 4 e ^{y}}

Solve for

y, x = \frac{e ^{y}}{1 + 4 e ^{y}}

ln (- \frac{x}{4 x - 1})

f (x) = - 3 y + 2 x = 2 (- 3 + x)

2 cos (2 x - 1) + 4

g (x) = - 2 (x - 4)

f (x) = x + 13

x^{2} + 5 x - 14

What is the inverse of f(x)=(e^x)/(1+4e^x) ?
The inverse of f(x)=(e^x)/(1+4e^x) is ln(-x/(4x-1))