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

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

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

inverse

y = \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) = 2 x^{3} - 11

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

f (x) = x^{2} - 11 x + 24

f (x) = 300 \cdot 4^{t}

- 2 x^{2}

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