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

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

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inverse of f(x)=ln((2x-1)/(x+2))

inverse

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

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

Solution steps

y = ln (\frac{2 x - 1}{x + 2})

Replace

x

with

y

x = ln (\frac{2 y - 1}{y + 2})

Solve for

y, x = ln (\frac{2 y - 1}{y + 2})

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

- 2 ln (x)

f (x) = \frac{2 x + 5}{4 x - 3}

\frac{3 x}{x - 8}

y = 3 x + 3

f (x) = 1 + 2 + 7 x

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