What is the inverse of f(x)=(e^x-7)/(e^x+2) ?

The inverse of f(x)=(e^x-7)/(e^x+2) is ln((-7-2x)/(x-1))

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inverse of f(x)=(e^x-7)/(e^x+2)

inverse

f (x) = \frac{e ^{x} - 7}{e ^{x} + 2}

ln (\frac{- 7 - 2 x}{x - 1})

Solution steps

y = \frac{e ^{x} - 7}{e ^{x} + 2}

Replace

x

with

y

x = \frac{e ^{y} - 7}{e ^{y} + 2}

Solve for

y, x = \frac{e ^{y} - 7}{e ^{y} + 2}

ln (\frac{- 7 - 2 x}{x - 1})

\frac{7 x + 5}{x + 9} + \frac{8 x - 10}{x + 9}

f (x) = e^{x} + 5

f (x) = 12 + 5 x - 5

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

f (x) = 600 - 2 x^{2}

What is the inverse of f(x)=(e^x-7)/(e^x+2) ?
The inverse of f(x)=(e^x-7)/(e^x+2) is ln((-7-2x)/(x-1))