What is the inverse of f(x)=(e^x)/(7+4e^x) ?

The inverse of f(x)=(e^x)/(7+4e^x) is ln(-(7x)/(4x-1))

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inverse of f(x)=(e^x)/(7+4e^x)

inverse

f (x) = \frac{e ^{x}}{7 + 4 e ^{x}}

ln (- \frac{7 x}{4 x - 1})

Solution steps

y = \frac{e ^{x}}{7 + 4 e ^{x}}

Replace

x

with

y

x = \frac{e ^{y}}{7 + 4 e ^{y}}

Solve for

y, x = \frac{e ^{y}}{7 + 4 e ^{y}}

ln (- \frac{7 x}{4 x - 1})

f (x) = 13 x - 7

\frac{5 x - 3}{2 x + 3}

x^{2} + 7 x + 10

\frac{4 - 11 x}{4 - 2 x}

f (x) = 11 x - 5

What is the inverse of f(x)=(e^x)/(7+4e^x) ?
The inverse of f(x)=(e^x)/(7+4e^x) is ln(-(7x)/(4x-1))