What is the inverse of f(x)=(e^x)/(e^x+3) ?

The inverse of f(x)=(e^x)/(e^x+3) is ln(-(3x)/(x-1))

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inverse of f(x)=(e^x)/(e^x+3)

inverse

f (x) = \frac{e ^{x}}{e ^{x} + 3}

ln (- \frac{3 x}{x - 1})

Solution steps

y = \frac{e ^{x}}{e ^{x} + 3}

Replace

x

with

y

x = \frac{e ^{y}}{e ^{y} + 3}

Solve for

y, x = \frac{e ^{y}}{e ^{y} + 3}

ln (- \frac{3 x}{x - 1})

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

3^{x + 9}

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

f (x) = \frac{- 4 x + 10}{- x - 1}

4 ln (x^{2} + 2 x + 1)

What is the inverse of f(x)=(e^x)/(e^x+3) ?
The inverse of f(x)=(e^x)/(e^x+3) is ln(-(3x)/(x-1))