What is the inverse of f(x)=(e^x)/(5+2e^x) ?

The inverse of f(x)=(e^x)/(5+2e^x) is ln(-(5x)/(2x-1))

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inverse of f(x)=(e^x)/(5+2e^x)

inverse

f (x) = \frac{e ^{x}}{5 + 2 e ^{x}}

ln (- \frac{5 x}{2 x - 1})

Solution steps

y = \frac{e ^{x}}{5 + 2 e ^{x}}

Replace

x

with

y

x = \frac{e ^{y}}{5 + 2 e ^{y}}

Solve for

y, x = \frac{e ^{y}}{5 + 2 e ^{y}}

ln (- \frac{5 x}{2 x - 1})

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

ln (13 x + 4)

f (x) = 5 x^{2} - 10 x + 4

f (x) = 9 lo g_{e} (9 x + 9)

- \frac{x + 6}{13}

What is the inverse of f(x)=(e^x)/(5+2e^x) ?
The inverse of f(x)=(e^x)/(5+2e^x) is ln(-(5x)/(2x-1))