What is the inverse of f(x)=(e^x)/(9+4e^x) ?

The inverse of f(x)=(e^x)/(9+4e^x) is ln(-(9x)/(4x-1))

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inverse of f(x)=(e^x)/(9+4e^x)

inverse

f (x) = \frac{e ^{x}}{9 + 4 e ^{x}}

ln (- \frac{9 x}{4 x - 1})

Solution steps

y = \frac{e ^{x}}{9 + 4 e ^{x}}

Replace

x

with

y

x = \frac{e ^{y}}{9 + 4 e ^{y}}

Solve for

y, x = \frac{e ^{y}}{9 + 4 e ^{y}}

ln (- \frac{9 x}{4 x - 1})

f (x) = \frac{2 x + 7}{3 x - 8}

f (x) = \frac{3}{2} x - 5

f (x) = (4 x - 1)^{2}

f (x) = \frac{4 x ^{2} - 1}{5 - 7 x ^{2}}

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

What is the inverse of f(x)=(e^x)/(9+4e^x) ?
The inverse of f(x)=(e^x)/(9+4e^x) is ln(-(9x)/(4x-1))