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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = 2 π r^{2} + 16 π r

f (x) = (x - 1)^{2} + (y - 2)^{2} = 64

f (x) = \frac{2}{x - 4} + 3

f (x) = x - 1 + 4

f (x) = 2 π x^{2} + 8 π x

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