What is the inverse of f(x)=(e^x)/(1+2e^x) ?

The inverse of f(x)=(e^x)/(1+2e^x) is ln(-x/(2x-1))

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inverse of f(x)=(e^x)/(1+2e^x)

inverse

f (x) = \frac{e ^{x}}{1 + 2 e ^{x}}

ln (- \frac{x}{2 x - 1})

Solution steps

y = \frac{e ^{x}}{1 + 2 e ^{x}}

Replace

x

with

y

x = \frac{e ^{y}}{1 + 2 e ^{y}}

Solve for

y, x = \frac{e ^{y}}{1 + 2 e ^{y}}

ln (- \frac{x}{2 x - 1})

f (x) = \frac{8 x}{0.3 x ^{2} + 4.1} - 0.1

f (x) = - x^{2} + 1

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

5 - x

f (x) = 3 x^{2}

What is the inverse of f(x)=(e^x)/(1+2e^x) ?
The inverse of f(x)=(e^x)/(1+2e^x) is ln(-x/(2x-1))