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

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

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inverse of f(x)=ln(x/(x+2))

inverse

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

- \frac{2 e ^{x}}{e ^{x} - 1}

Solution steps

y = ln (\frac{x}{x + 2})

Replace

x

with

y

x = ln (\frac{y}{y + 2})

Solve for

y, x = ln (\frac{y}{y + 2})

- \frac{2 e ^{x}}{e ^{x} - 1}

f (x) = 2 x^{2} - 8 x - 3

\frac{3}{4} x + 7

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

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

f (x) = 8 - 8 - x

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